From 61b3b174527ae91ca9fe1e59b0de4932d9d4e70a Mon Sep 17 00:00:00 2001 From: Kss2k Date: Tue, 15 Oct 2024 18:32:57 +0000 Subject: [PATCH] Update pkgdown site [skip ci] --- index.html | 2 +- pkgdown.yml | 2 +- search.json | 2 +- 3 files changed, 3 insertions(+), 3 deletions(-) diff --git a/index.html b/index.html index 346f68f..5cc7d4b 100644 --- a/index.html +++ b/index.html @@ -63,7 +63,7 @@

modsem

-

This is a package which allows you to perform interactions between latent variables (i.e., moderation) in CB-SEM. See https://kss2k.github.io/modsem/ for a tutorial.

+

This is a package which allows you to perform interactions between latent variables (i.e., moderation) in CB-SEM. See https://www.modsem.org for a tutorial.

To Install diff --git a/pkgdown.yml b/pkgdown.yml index 29a7fb8..dd1f199 100644 --- a/pkgdown.yml +++ b/pkgdown.yml @@ -11,4 +11,4 @@ articles: observed_lms_qml: observed_lms_qml.html plot_interactions: plot_interactions.html quadratic: quadratic.html -last_built: 2024-10-15T17:28Z +last_built: 2024-10-15T18:20Z diff --git a/search.json b/search.json index 80c9f41..746db93 100644 --- a/search.json +++ b/search.json @@ -1 +1 @@ -[{"path":"/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"MIT License","title":"MIT License","text":"Copyright (c) 2024 modsem authors Permission hereby granted, free charge, person obtaining copy software associated documentation files (“Software”), deal Software without restriction, including without limitation rights use, copy, modify, merge, publish, distribute, sublicense, /sell copies Software, permit persons Software furnished , subject following conditions: copyright notice permission notice shall included copies substantial portions Software. SOFTWARE PROVIDED “”, WITHOUT WARRANTY KIND, EXPRESS IMPLIED, INCLUDING LIMITED WARRANTIES MERCHANTABILITY, FITNESS PARTICULAR PURPOSE NONINFRINGEMENT. EVENT SHALL AUTHORS COPYRIGHT HOLDERS LIABLE CLAIM, DAMAGES LIABILITY, WHETHER ACTION CONTRACT, TORT OTHERWISE, ARISING , CONNECTION SOFTWARE USE DEALINGS SOFTWARE.","code":""},{"path":"/articles/customizing.html","id":"specifying-the-measurement-model","dir":"Articles","previous_headings":"","what":"Specifying The Measurement Model","title":"customizing interaction terms","text":"default, modsem() creates possible combinations different product indicators. However, another common approach match indicators order. example, let’s say interaction laten variables X Z: ‘X =~ x1 + x2’ ‘Z =~ z1 + z2’. default get ‘XZ =~ x1z1 + x1z2 + x2z1 + x2z2’. wanted use matching approach want get ‘XZ =~ x1z1 + x2z2’ instead. achieve can use ‘match = TRUE’ argument.","code":"m2 <- ' # Outer Model X =~ x1 + x2 Y =~ y1 + y2 Z =~ z1 + z2 # Inner model Y ~ X + Z + X:Z ' est2 <- modsem(m2, oneInt, match = TRUE) summary(est2) #> modsem: #> Method = dblcent #> lavaan 0.6-19 ended normally after 41 iterations #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 22 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 11.355 #> Degrees of freedom 14 #> P-value (Chi-square) 0.658 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Latent Variables: #> Estimate Std.Err z-value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.819 0.021 38.127 0.000 #> Y =~ #> y1 1.000 #> y2 0.807 0.010 82.495 0.000 #> Z =~ #> z1 1.000 #> z2 0.836 0.024 35.392 0.000 #> XZ =~ #> x1z1 1.000 #> x2z2 0.645 0.024 26.904 0.000 #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> Y ~ #> X 0.688 0.029 23.366 0.000 #> Z 0.576 0.029 20.173 0.000 #> XZ 0.706 0.032 22.405 0.000 #> #> Covariances: #> Estimate Std.Err z-value P(>|z|) #> .x1z1 ~~ #> .x2z2 0.000 #> X ~~ #> Z 0.202 0.025 8.182 0.000 #> XZ 0.003 0.026 0.119 0.905 #> Z ~~ #> XZ 0.042 0.026 1.621 0.105 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .x1 0.179 0.022 8.029 0.000 #> .x2 0.151 0.015 9.956 0.000 #> .y1 0.184 0.021 8.577 0.000 #> .y2 0.136 0.014 9.663 0.000 #> .z1 0.197 0.025 7.802 0.000 #> .z2 0.138 0.018 7.831 0.000 #> .x1z1 0.319 0.035 9.141 0.000 #> .x2z2 0.244 0.016 15.369 0.000 #> X 0.962 0.042 23.120 0.000 #> .Y 0.964 0.042 23.110 0.000 #> Z 0.987 0.044 22.260 0.000 #> XZ 1.041 0.054 19.441 0.000"},{"path":"/articles/customizing.html","id":"more-complicated-models","dir":"Articles","previous_headings":"","what":"More complicated models","title":"customizing interaction terms","text":"want even control can use get_pi_syntax() get_pi_data() functions, can extract modified syntax data modsem, alter accordingly. can particularly useful cases want estimate model using feature lavaan, isn’t available modsem. example, (yet) syntax ordered- multigroup models isn’t flexible lavaan. Thus can modify auto-generated syntax (altered dataset) modsem suit needs.","code":"m3 <- ' # Outer Model X =~ x1 + x2 Y =~ y1 + y2 Z =~ z1 + z2 # Inner model Y ~ X + Z + X:Z ' syntax <- get_pi_syntax(m3) cat(syntax) #> X =~ x1 #> X =~ x2 #> Y =~ y1 #> Y =~ y2 #> Z =~ z1 #> Z =~ z2 #> Y ~ X #> Y ~ Z #> Y ~ XZ #> XZ =~ 1*x1z1 #> XZ =~ x2z1 #> XZ =~ x1z2 #> XZ =~ x2z2 #> x1z1 ~~ 0*x2z2 #> x1z2 ~~ 0*x2z1 #> x1z1 ~~ x1z2 #> x1z1 ~~ x2z1 #> x1z2 ~~ x2z2 #> x2z1 ~~ x2z2 data <- get_pi_data(m3, oneInt) head(data) #> x1 x2 y1 y2 z1 z2 x1z1 #> 1 2.4345722 1.3578655 1.4526897 0.9560888 0.8184825 1.60708140 -0.4823019 #> 2 0.2472734 0.2723201 0.5496756 0.7115311 3.6649148 2.60983102 -2.2680403 #> 3 -1.3647759 -0.5628205 -0.9835467 -0.6697747 1.7249386 2.10981827 -1.9137416 #> 4 3.0432836 2.2153763 6.4641465 4.7805981 2.5697116 3.26335379 2.9385205 #> 5 2.8148841 2.7029616 2.2860280 2.1457643 0.3467850 0.07164577 -1.4009548 #> 6 -0.5453450 -0.7530642 1.1294876 1.1998472 -0.2362958 0.60252657 1.7465860 #> x2z1 x1z2 x2z2 #> 1 -0.1884837 0.3929380 -0.0730934 #> 2 -2.6637694 -1.2630544 -1.4547433 #> 3 -1.4299711 -2.3329864 -1.7383407 #> 4 1.3971422 3.9837389 1.9273102 #> 5 -1.1495704 -2.2058995 -1.8169042 #> 6 2.2950753 0.7717365 1.0568143"},{"path":"/articles/interaction_two_etas.html","id":"the-problem","dir":"Articles","previous_headings":"","what":"The Problem","title":"interaction effects between endogenous variables","text":"Interaction effects two endogenous (.e., dependent) variables work expect product indicator methods (\"dblcent\", \"rca\", \"ca\", \"uca\"). lms- qml approach however, straight forward. lms- qml approach can (default) handle interaction effects endogenous exogenous (.e., independent) variables, interaction effects two endogenous variables. interaction effect two endogenous variables, equations easily written ‘reduced’ form – meaning normal estimation procedures won’t work.","code":""},{"path":"/articles/interaction_two_etas.html","id":"the-solution","dir":"Articles","previous_headings":"","what":"The Solution","title":"interaction effects between endogenous variables","text":"said, work-around limitations lms- qml-approach. essence, model can split two parts, one linear one non-linear. Basically, can replace covariance matrix used estimation non-linear model, model-implied covariance matrix linear model. Thus can treat endogenous variable exogenous – given can expressed linear model.","code":""},{"path":"/articles/interaction_two_etas.html","id":"example","dir":"Articles","previous_headings":"","what":"Example","title":"interaction effects between endogenous variables","text":"Let’s consider theory planned behaviour (TPB) wish estimate quadratic effect INT BEH (INT:INT). following model: Since INT endogenous variable, quadratic term (.e., interaction effect ) include two endogenous variables. Thus ordinarily able estimate model using lms- qml-approach. However, can split model two parts, one linear one non-linear. INT endogenous variable, can expressed linear model – since affected interaction terms: remove part original model, giving us: now just estimate non-linear model, since INT now exogenous variable. however incorporate structural model INT. address , can make modsem replace covariance matrix (phi) (INT, PBC, ATT, SN) model-implied covariance matrix linear model, whilst estimating models simultaneously. acheive , can use cov.syntax argument modsem:","code":"tpb <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ INT:INT ' tpb_linear <- 'INT ~ PBC + ATT + SN' tpb_nonlinear <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) BEH ~ INT + PBC BEH ~ INT:INT ' est_lms <- modsem(tpb_nonlinear, data = TPB, cov.syntax = tpb_linear, method = \"lms\") #> Warning: It is recommended that you have at least 48 nodes for interaction #> effects between endogenous variables in the lms approach 'nodes = 24' summary(est_lms) #> Estimating null model #> EM: Iteration = 1, LogLik = -28467.33, Change = -28467.332 #> EM: Iteration = 2, LogLik = -28124.48, Change = 342.852 #> EM: Iteration = 3, LogLik = -27825.10, Change = 299.377 #> EM: Iteration = 4, LogLik = -27581.12, Change = 243.980 #> EM: Iteration = 5, LogLik = -27370.69, Change = 210.431 #> EM: Iteration = 6, LogLik = -27175.43, Change = 195.264 #> EM: Iteration = 7, LogLik = -27000.48, Change = 174.946 #> EM: Iteration = 8, LogLik = -26848.56, Change = 151.919 #> EM: Iteration = 9, LogLik = -26711.51, Change = 137.051 #> EM: Iteration = 10, LogLik = -26592.54, Change = 118.968 #> EM: Iteration = 11, LogLik = -26504.04, Change = 88.504 #> EM: Iteration = 12, LogLik = -26466.85, Change = 37.190 #> EM: Iteration = 13, LogLik = -26452.38, Change = 14.465 #> EM: Iteration = 14, LogLik = -26439.05, Change = 13.331 #> EM: Iteration = 15, LogLik = -26430.51, Change = 8.541 #> EM: Iteration = 16, LogLik = -26422.81, Change = 7.698 #> EM: Iteration = 17, LogLik = -26403.89, Change = 18.924 #> EM: Iteration = 18, LogLik = -26402.25, Change = 1.642 #> EM: Iteration = 19, LogLik = -26401.21, Change = 1.037 #> EM: Iteration = 20, LogLik = -26400.26, Change = 0.955 #> EM: Iteration = 21, LogLik = -26399.30, Change = 0.960 #> EM: Iteration = 22, LogLik = -26398.64, Change = 0.658 #> EM: Iteration = 23, LogLik = -26398.02, Change = 0.615 #> EM: Iteration = 24, LogLik = -26397.74, Change = 0.278 #> EM: Iteration = 25, LogLik = -26397.33, Change = 0.420 #> EM: Iteration = 26, LogLik = -26397.20, Change = 0.128 #> EM: Iteration = 27, LogLik = -26396.77, Change = 0.425 #> EM: Iteration = 28, LogLik = -26396.48, Change = 0.292 #> EM: Iteration = 29, LogLik = -26396.34, Change = 0.145 #> EM: Iteration = 30, LogLik = -26396.31, Change = 0.022 #> EM: Iteration = 31, LogLik = -26395.95, Change = 0.365 #> EM: Iteration = 32, LogLik = -26395.73, Change = 0.215 #> EM: Iteration = 33, LogLik = -26395.68, Change = 0.055 #> EM: Iteration = 34, LogLik = -26395.37, Change = 0.304 #> EM: Iteration = 35, LogLik = -26395.30, Change = 0.079 #> EM: Iteration = 36, LogLik = -26395.10, Change = 0.198 #> EM: Iteration = 37, LogLik = -26395.04, Change = 0.057 #> EM: Iteration = 38, LogLik = -26394.99, Change = 0.054 #> EM: Iteration = 39, LogLik = -26394.96, Change = 0.028 #> EM: Iteration = 40, LogLik = -26394.93, Change = 0.031 #> EM: Iteration = 41, LogLik = -26394.91, Change = 0.019 #> EM: Iteration = 42, LogLik = -26394.89, Change = 0.023 #> EM: Iteration = 43, LogLik = -26394.87, Change = 0.015 #> EM: Iteration = 44, LogLik = -26394.85, Change = 0.019 #> EM: Iteration = 45, LogLik = -26394.84, Change = 0.013 #> EM: Iteration = 46, LogLik = -26394.82, Change = 0.018 #> EM: Iteration = 47, LogLik = -26394.81, Change = 0.012 #> EM: Iteration = 48, LogLik = -26394.79, Change = 0.018 #> EM: Iteration = 49, LogLik = -26394.78, Change = 0.013 #> EM: Iteration = 50, LogLik = -26394.76, Change = 0.020 #> EM: Iteration = 51, LogLik = -26394.74, Change = 0.015 #> EM: Iteration = 52, LogLik = -26394.72, Change = 0.028 #> EM: Iteration = 53, LogLik = -26394.69, Change = 0.022 #> EM: Iteration = 54, LogLik = -26394.63, Change = 0.062 #> EM: Iteration = 55, LogLik = -26394.58, Change = 0.057 #> EM: Iteration = 56, LogLik = -26394.29, Change = 0.284 #> EM: Iteration = 57, LogLik = -26394.04, Change = 0.248 #> EM: Iteration = 58, LogLik = -26393.97, Change = 0.075 #> EM: Iteration = 59, LogLik = -26393.73, Change = 0.240 #> EM: Iteration = 60, LogLik = -26393.72, Change = 0.011 #> EM: Iteration = 61, LogLik = -26393.71, Change = 0.013 #> EM: Iteration = 62, LogLik = -26393.70, Change = 0.005 #> EM: Iteration = 63, LogLik = -26393.69, Change = 0.008 #> EM: Iteration = 64, LogLik = -26393.69, Change = 0.003 #> EM: Iteration = 65, LogLik = -26393.68, Change = 0.007 #> EM: Iteration = 66, LogLik = -26393.68, Change = 0.003 #> EM: Iteration = 67, LogLik = -26393.67, Change = 0.007 #> EM: Iteration = 68, LogLik = -26393.67, Change = 0.003 #> EM: Iteration = 69, LogLik = -26393.66, Change = 0.006 #> EM: Iteration = 70, LogLik = -26393.66, Change = 0.002 #> EM: Iteration = 71, LogLik = -26393.66, Change = 0.006 #> EM: Iteration = 72, LogLik = -26393.65, Change = 0.002 #> EM: Iteration = 73, LogLik = -26393.65, Change = 0.005 #> EM: Iteration = 74, LogLik = -26393.65, Change = 0.002 #> EM: Iteration = 75, LogLik = -26393.64, Change = 0.005 #> EM: Iteration = 76, LogLik = -26393.64, Change = 0.002 #> EM: Iteration = 77, LogLik = -26393.63, Change = 0.004 #> EM: Iteration = 78, LogLik = -26393.63, Change = 0.002 #> EM: Iteration = 79, LogLik = -26393.63, Change = 0.004 #> EM: Iteration = 80, LogLik = -26393.63, Change = 0.002 #> EM: Iteration = 81, LogLik = -26393.62, Change = 0.004 #> EM: Iteration = 82, LogLik = -26393.62, Change = 0.002 #> EM: Iteration = 83, LogLik = -26393.62, Change = 0.004 #> EM: Iteration = 84, LogLik = -26393.61, Change = 0.002 #> EM: Iteration = 85, LogLik = -26393.61, Change = 0.003 #> EM: Iteration = 86, LogLik = -26393.61, Change = 0.002 #> EM: Iteration = 87, LogLik = -26393.60, Change = 0.003 #> EM: Iteration = 88, LogLik = -26393.60, Change = 0.003 #> EM: Iteration = 89, LogLik = -26393.60, Change = 0.003 #> EM: Iteration = 90, LogLik = -26393.60, Change = 0.003 #> EM: Iteration = 91, LogLik = -26393.59, Change = 0.003 #> EM: Iteration = 92, LogLik = -26393.59, Change = 0.003 #> EM: Iteration = 93, LogLik = -26393.59, Change = 0.003 #> EM: Iteration = 94, LogLik = -26393.59, Change = 0.003 #> EM: Iteration = 95, LogLik = -26393.58, Change = 0.003 #> EM: Iteration = 96, LogLik = -26393.58, Change = 0.003 #> EM: Iteration = 97, LogLik = -26393.58, Change = 0.002 #> EM: Iteration = 98, LogLik = -26393.58, Change = 0.003 #> EM: Iteration = 99, LogLik = -26393.57, Change = 0.002 #> EM: Iteration = 100, LogLik = -26393.57, Change = 0.003 #> EM: Iteration = 101, LogLik = -26393.57, Change = 0.002 #> EM: Iteration = 102, LogLik = -26393.57, Change = 0.003 #> EM: Iteration = 103, LogLik = -26393.56, Change = 0.002 #> EM: Iteration = 104, LogLik = -26393.56, Change = 0.003 #> EM: Iteration = 105, LogLik = -26393.56, Change = 0.002 #> EM: Iteration = 106, LogLik = -26393.56, Change = 0.003 #> EM: Iteration = 107, LogLik = -26393.55, Change = 0.002 #> EM: Iteration = 108, LogLik = -26393.55, Change = 0.003 #> EM: Iteration = 109, LogLik = -26393.55, Change = 0.002 #> EM: Iteration = 110, LogLik = -26393.55, Change = 0.003 #> EM: Iteration = 111, LogLik = -26393.54, Change = 0.002 #> EM: Iteration = 112, LogLik = -26393.54, Change = 0.003 #> EM: Iteration = 113, LogLik = -26393.54, Change = 0.002 #> EM: Iteration = 114, LogLik = -26393.54, Change = 0.003 #> EM: Iteration = 115, LogLik = -26393.53, Change = 0.002 #> EM: Iteration = 116, LogLik = -26393.53, Change = 0.003 #> EM: Iteration = 117, LogLik = -26393.53, Change = 0.002 #> EM: Iteration = 118, LogLik = -26393.53, Change = 0.003 #> EM: Iteration = 119, LogLik = -26393.53, Change = 0.001 #> EM: Iteration = 120, LogLik = -26393.52, Change = 0.003 #> EM: Iteration = 121, LogLik = -26393.52, Change = 0.001 #> EM: Iteration = 122, LogLik = -26393.52, Change = 0.003 #> EM: Iteration = 123, LogLik = -26393.52, Change = 0.001 #> EM: Iteration = 124, LogLik = -26393.51, Change = 0.003 #> EM: Iteration = 125, LogLik = -26393.51, Change = 0.001 #> EM: Iteration = 126, LogLik = -26393.51, Change = 0.003 #> EM: Iteration = 127, LogLik = -26393.51, Change = 0.001 #> EM: Iteration = 128, LogLik = -26393.51, Change = 0.003 #> EM: Iteration = 129, LogLik = -26393.50, Change = 0.001 #> EM: Iteration = 130, LogLik = -26393.50, Change = 0.003 #> EM: Iteration = 131, LogLik = -26393.50, Change = 0.001 #> EM: Iteration = 132, LogLik = -26393.50, Change = 0.003 #> EM: Iteration = 133, LogLik = -26393.50, Change = 0.001 #> EM: Iteration = 134, LogLik = -26393.49, Change = 0.003 #> EM: Iteration = 135, LogLik = -26393.49, Change = 0.001 #> EM: Iteration = 136, LogLik = -26393.49, Change = 0.003 #> EM: Iteration = 137, LogLik = -26393.49, Change = 0.001 #> EM: Iteration = 138, LogLik = -26393.48, Change = 0.003 #> EM: Iteration = 139, LogLik = -26393.48, Change = 0.001 #> EM: Iteration = 140, LogLik = -26393.48, Change = 0.003 #> EM: Iteration = 141, LogLik = -26393.48, Change = 0.001 #> EM: Iteration = 142, LogLik = -26393.48, Change = 0.003 #> EM: Iteration = 143, LogLik = -26393.48, Change = 0.001 #> EM: Iteration = 144, LogLik = -26393.47, Change = 0.003 #> EM: Iteration = 145, LogLik = -26393.47, Change = 0.001 #> EM: Iteration = 146, LogLik = -26393.47, Change = 0.003 #> EM: Iteration = 147, LogLik = -26393.47, Change = 0.000 #> EM: Iteration = 148, LogLik = -26393.46, Change = 0.003 #> EM: Iteration = 149, LogLik = -26393.46, Change = 0.000 #> EM: Iteration = 150, LogLik = -26393.46, Change = 0.003 #> EM: Iteration = 151, LogLik = -26393.46, Change = 0.000 #> EM: Iteration = 152, LogLik = -26393.46, Change = 0.004 #> EM: Iteration = 153, LogLik = -26393.46, Change = 0.000 #> EM: Iteration = 154, LogLik = -26393.45, Change = 0.004 #> EM: Iteration = 155, LogLik = -26393.45, Change = 0.000 #> EM: Iteration = 156, LogLik = -26393.45, Change = 0.004 #> EM: Iteration = 157, LogLik = -26393.45, Change = 0.000 #> #> modsem (version 1.0.3): #> Estimator LMS #> Optimization method EM-NLMINB #> Number of observations 2000 #> Number of iterations 136 #> Loglikelihood -23781.36 #> Akaike (AIC) 47670.72 #> Bayesian (BIC) 47973.16 #> #> Numerical Integration: #> Points of integration (per dim) 24 #> Dimensions 1 #> Total points of integration 24 #> #> Fit Measures for H0: #> Loglikelihood -26393 #> Akaike (AIC) 52892.89 #> Bayesian (BIC) 53189.74 #> Chi-square 66.72 #> Degrees of Freedom (Chi-square) 82 #> P-value (Chi-square) 0.889 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 2612.09 #> Difference test (D) 5224.18 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> BEH 0.235 #> INT 0.365 #> R-Squared Null-Model (H0): #> BEH 0.210 #> INT 0.367 #> R-Squared Change: #> BEH 0.025 #> INT -0.002 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information expected #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> INT =~ #> int1 1.000 #> int2 0.915 0.015 59.13 0.000 #> int3 0.807 0.015 55.25 0.000 #> ATT =~ #> att1 1.000 #> att2 0.876 0.012 71.52 0.000 #> att3 0.787 0.012 66.56 0.000 #> att4 0.693 0.011 60.51 0.000 #> att5 0.885 0.012 71.68 0.000 #> SN =~ #> sn1 1.000 #> sn2 0.893 0.017 52.63 0.000 #> PBC =~ #> pbc1 1.000 #> pbc2 0.912 0.013 69.17 0.000 #> pbc3 0.801 0.012 66.55 0.000 #> BEH =~ #> b1 1.000 #> b2 0.959 0.030 32.01 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> BEH ~ #> INT 0.196 0.025 7.72 0.000 #> PBC 0.238 0.022 10.66 0.000 #> INT:INT 0.129 0.017 7.43 0.000 #> INT ~ #> PBC 0.218 0.029 7.54 0.000 #> ATT 0.210 0.025 8.32 0.000 #> SN 0.172 0.028 6.25 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> int1 1.005 0.022 46.65 0.000 #> int2 1.004 0.020 50.31 0.000 #> int3 0.998 0.018 54.37 0.000 #> att1 1.007 0.025 40.32 0.000 #> att2 1.001 0.022 45.02 0.000 #> att3 1.011 0.020 49.61 0.000 #> att4 0.994 0.019 53.44 0.000 #> att5 0.986 0.022 43.87 0.000 #> sn1 1.000 0.025 39.96 0.000 #> sn2 1.005 0.022 44.71 0.000 #> pbc1 0.991 0.025 40.38 0.000 #> pbc2 0.979 0.023 42.87 0.000 #> pbc3 0.986 0.020 48.34 0.000 #> b1 0.995 0.024 41.61 0.000 #> b2 1.014 0.022 45.15 0.000 #> BEH 0.000 #> INT 0.000 #> ATT 0.000 #> SN 0.000 #> PBC 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> PBC ~~ #> ATT 0.668 0.079 8.48 0.000 #> SN 0.675 0.054 12.48 0.000 #> ATT ~~ #> SN 0.625 0.029 21.63 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> int1 0.161 0.009 18.33 0.000 #> int2 0.161 0.008 20.89 0.000 #> int3 0.170 0.007 23.48 0.000 #> att1 0.167 0.007 23.23 0.000 #> att2 0.150 0.006 24.81 0.000 #> att3 0.160 0.006 26.51 0.000 #> att4 0.163 0.006 27.46 0.000 #> att5 0.159 0.006 24.85 0.000 #> sn1 0.181 0.015 12.48 0.000 #> sn2 0.155 0.012 13.28 0.000 #> pbc1 0.145 0.008 18.27 0.000 #> pbc2 0.160 0.007 21.74 0.000 #> pbc3 0.154 0.007 23.70 0.000 #> b1 0.185 0.019 9.76 0.000 #> b2 0.136 0.017 7.97 0.000 #> BEH 0.475 0.023 20.47 0.000 #> PBC 0.960 0.037 26.14 0.000 #> ATT 1.000 0.058 17.32 0.000 #> SN 0.968 0.086 11.29 0.000 #> INT 0.481 0.019 24.99 0.000 est_qml <- modsem(tpb_nonlinear, data = TPB, cov.syntax = tpb_linear, method = \"qml\") summary(est_qml) #> Estimating null model #> Starting M-step #> #> modsem (version 1.0.3): #> Estimator QML #> Optimization method NLMINB #> Number of observations 2000 #> Number of iterations 76 #> Loglikelihood -26360.52 #> Akaike (AIC) 52829.04 #> Bayesian (BIC) 53131.49 #> #> Fit Measures for H0: #> Loglikelihood -26393 #> Akaike (AIC) 52892.45 #> Bayesian (BIC) 53189.29 #> Chi-square 66.27 #> Degrees of Freedom (Chi-square) 82 #> P-value (Chi-square) 0.897 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 32.70 #> Difference test (D) 65.41 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> BEH 0.239 #> INT 0.370 #> R-Squared Null-Model (H0): #> BEH 0.210 #> INT 0.367 #> R-Squared Change: #> BEH 0.029 #> INT 0.003 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information observed #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> INT =~ #> int1 1.000 #> int2 0.914 0.015 59.04 0.000 #> int3 0.807 0.015 55.65 0.000 #> ATT =~ #> att1 1.000 #> att2 0.878 0.012 71.56 0.000 #> att3 0.789 0.012 66.37 0.000 #> att4 0.695 0.011 61.00 0.000 #> att5 0.887 0.013 70.85 0.000 #> SN =~ #> sn1 1.000 #> sn2 0.888 0.017 52.62 0.000 #> PBC =~ #> pbc1 1.000 #> pbc2 0.913 0.013 69.38 0.000 #> pbc3 0.801 0.012 66.08 0.000 #> BEH =~ #> b1 1.000 #> b2 0.960 0.032 29.91 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> BEH ~ #> INT 0.197 0.025 7.76 0.000 #> PBC 0.239 0.023 10.59 0.000 #> INT:INT 0.128 0.016 7.88 0.000 #> INT ~ #> PBC 0.222 0.030 7.51 0.000 #> ATT 0.213 0.026 8.17 0.000 #> SN 0.175 0.028 6.33 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> int1 1.014 0.022 46.96 0.000 #> int2 1.012 0.020 50.41 0.000 #> int3 1.005 0.018 54.80 0.000 #> att1 1.014 0.024 42.01 0.000 #> att2 1.007 0.021 46.97 0.000 #> att3 1.016 0.020 51.45 0.000 #> att4 0.999 0.018 55.65 0.000 #> att5 0.992 0.022 45.67 0.000 #> sn1 1.006 0.024 41.66 0.000 #> sn2 1.010 0.022 46.71 0.000 #> pbc1 0.998 0.024 42.41 0.000 #> pbc2 0.985 0.022 44.93 0.000 #> pbc3 0.991 0.020 50.45 0.000 #> b1 0.999 0.023 42.64 0.000 #> b2 1.017 0.022 46.25 0.000 #> BEH 0.000 #> INT 0.000 #> ATT 0.000 #> SN 0.000 #> PBC 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> PBC ~~ #> ATT 0.678 0.029 23.45 0.000 #> SN 0.678 0.029 23.08 0.000 #> ATT ~~ #> SN 0.629 0.029 21.70 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> int1 0.158 0.009 18.22 0.000 #> int2 0.160 0.008 20.38 0.000 #> int3 0.168 0.007 23.63 0.000 #> att1 0.167 0.007 23.53 0.000 #> att2 0.150 0.006 24.71 0.000 #> att3 0.160 0.006 26.38 0.000 #> att4 0.162 0.006 27.64 0.000 #> att5 0.159 0.006 24.93 0.000 #> sn1 0.178 0.015 12.09 0.000 #> sn2 0.157 0.012 13.26 0.000 #> pbc1 0.145 0.008 18.44 0.000 #> pbc2 0.160 0.007 21.42 0.000 #> pbc3 0.154 0.006 23.80 0.000 #> b1 0.185 0.020 9.42 0.000 #> b2 0.135 0.018 7.60 0.000 #> BEH 0.475 0.024 19.74 0.000 #> PBC 0.962 0.036 27.04 0.000 #> ATT 0.998 0.037 26.93 0.000 #> SN 0.988 0.039 25.23 0.000 #> INT 0.488 0.020 24.59 0.000"},{"path":"/articles/lms_qml.html","id":"the-latent-moderated-structural-equations-lms-and-the-quasi-maximum-likelihood-qml-approach","dir":"Articles","previous_headings":"","what":"The Latent Moderated Structural Equations (LMS) and the Quasi Maximum Likelihood (QML) approach","title":"LMS and QML approaches","text":"LMS- QML approach works models, interaction effects endogenous can bit tricky estimate (see vignette. approaches (particularily LMS approach) quite computationally intensive, thus partly implemented C++ (using Rcpp RcppArmadillo). Additionally starting parameters estimated using double centering approach (means observed variables) used generate good starting parameters faster convergence. want see progress estimation process can use ´verbose = TRUE´.","code":""},{"path":"/articles/lms_qml.html","id":"a-simple-example","dir":"Articles","previous_headings":"The Latent Moderated Structural Equations (LMS) and the Quasi Maximum Likelihood (QML) approach","what":"A Simple Example","title":"LMS and QML approaches","text":"can see example LMS approach simple model. default summary function calculates fit measures compared null model (.e., model without interaction term). can see example using QML approach.","code":"library(modsem) m1 <- ' # Outer Model X =~ x1 X =~ x2 + x3 Z =~ z1 + z2 + z3 Y =~ y1 + y2 + y3 # Inner model Y ~ X + Z Y ~ X:Z ' lms1 <- modsem(m1, oneInt, method = \"lms\") summary(lms1, standardized = TRUE) # standardized estimates #> Estimating null model #> EM: Iteration = 1, LogLik = -17831.87, Change = -17831.875 #> EM: Iteration = 2, LogLik = -17831.87, Change = 0.000 #> #> modsem (version 1.0.3): #> Estimator LMS #> Optimization method EM-NLMINB #> Number of observations 2000 #> Number of iterations 92 #> Loglikelihood -14687.85 #> Akaike (AIC) 29437.71 #> Bayesian (BIC) 29611.34 #> #> Numerical Integration: #> Points of integration (per dim) 24 #> Dimensions 1 #> Total points of integration 24 #> #> Fit Measures for H0: #> Loglikelihood -17832 #> Akaike (AIC) 35723.75 #> Bayesian (BIC) 35891.78 #> Chi-square 17.52 #> Degrees of Freedom (Chi-square) 24 #> P-value (Chi-square) 0.826 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 3144.02 #> Difference test (D) 6288.04 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> Y 0.596 #> R-Squared Null-Model (H0): #> Y 0.395 #> R-Squared Change: #> Y 0.201 #> #> Parameter Estimates: #> Coefficients standardized #> Information expected #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> X =~ #> x1 0.926 #> x2 0.891 0.014 65.27 0.000 #> x3 0.912 0.013 68.77 0.000 #> Z =~ #> z1 0.927 #> z2 0.898 0.014 65.55 0.000 #> z3 0.913 0.013 69.05 0.000 #> Y =~ #> y1 0.969 #> y2 0.954 0.009 106.30 0.000 #> y3 0.961 0.009 112.47 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> Y ~ #> X 0.427 0.020 20.89 0.000 #> Z 0.370 0.019 19.53 0.000 #> X:Z 0.454 0.017 26.72 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> X ~~ #> Z 0.199 0.027 7.29 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> x1 0.142 0.007 19.63 0.000 #> x2 0.206 0.009 24.10 0.000 #> x3 0.169 0.008 21.53 0.000 #> z1 0.141 0.008 18.74 0.000 #> z2 0.193 0.009 22.64 0.000 #> z3 0.167 0.008 20.78 0.000 #> y1 0.061 0.003 17.98 0.000 #> y2 0.090 0.004 22.74 0.000 #> y3 0.077 0.004 20.73 0.000 #> X 1.000 0.016 60.80 0.000 #> Z 1.000 0.018 54.92 0.000 #> Y 0.404 0.015 27.12 0.000 qml1 <- modsem(m1, oneInt, method = \"qml\") summary(qml1) #> Estimating null model #> Starting M-step #> #> modsem (version 1.0.3): #> Estimator QML #> Optimization method NLMINB #> Number of observations 2000 #> Number of iterations 111 #> Loglikelihood -17496.22 #> Akaike (AIC) 35054.43 #> Bayesian (BIC) 35228.06 #> #> Fit Measures for H0: #> Loglikelihood -17832 #> Akaike (AIC) 35723.75 #> Bayesian (BIC) 35891.78 #> Chi-square 17.52 #> Degrees of Freedom (Chi-square) 24 #> P-value (Chi-square) 0.826 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 335.66 #> Difference test (D) 671.32 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> Y 0.607 #> R-Squared Null-Model (H0): #> Y 0.395 #> R-Squared Change: #> Y 0.211 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information observed #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.803 0.013 63.96 0.000 #> x3 0.914 0.013 67.80 0.000 #> Z =~ #> z1 1.000 #> z2 0.810 0.012 65.12 0.000 #> z3 0.881 0.013 67.62 0.000 #> Y =~ #> y1 1.000 #> y2 0.798 0.007 107.57 0.000 #> y3 0.899 0.008 112.55 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> Y ~ #> X 0.674 0.032 20.94 0.000 #> Z 0.566 0.030 18.96 0.000 #> X:Z 0.712 0.028 25.45 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> x1 1.023 0.024 42.89 0.000 #> x2 1.215 0.020 60.99 0.000 #> x3 0.919 0.022 41.48 0.000 #> z1 1.012 0.024 41.57 0.000 #> z2 1.206 0.020 59.27 0.000 #> z3 0.916 0.022 42.06 0.000 #> y1 1.038 0.033 31.45 0.000 #> y2 1.221 0.027 45.49 0.000 #> y3 0.955 0.030 31.86 0.000 #> Y 0.000 #> X 0.000 #> Z 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> X ~~ #> Z 0.200 0.024 8.24 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> x1 0.158 0.009 18.14 0.000 #> x2 0.162 0.007 23.19 0.000 #> x3 0.165 0.008 20.82 0.000 #> z1 0.166 0.009 18.34 0.000 #> z2 0.159 0.007 22.62 0.000 #> z3 0.158 0.008 20.71 0.000 #> y1 0.159 0.009 17.98 0.000 #> y2 0.154 0.007 22.67 0.000 #> y3 0.164 0.008 20.71 0.000 #> X 0.983 0.036 26.99 0.000 #> Z 1.019 0.038 26.95 0.000 #> Y 0.943 0.038 24.87 0.000"},{"path":"/articles/lms_qml.html","id":"a-more-complicated-example","dir":"Articles","previous_headings":"The Latent Moderated Structural Equations (LMS) and the Quasi Maximum Likelihood (QML) approach","what":"A more complicated example","title":"LMS and QML approaches","text":"can see example complicated example using model theory planned behaviour (TPB), two endogenous variables, interaction endogenous exogenous variable. estimating complicated models LMS-approach, recommended increase number nodes used numerical integration. default number nodes set 16, can increased using nodes argument. argument effect QML approach. interaction effect endogenous exogenous variable, recommended use least 32 nodes LMS-approach. can also get robust standard errors setting robust.se = TRUE modsem() function. Note: want lms-approach give similar results possible mplus, increase number nodes (e.g., nodes = 100).","code":"# ATT = Attitude, # PBC = Perceived Behavioural Control # INT = Intention # SN = Subjective Norms # BEH = Behaviour tpb <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ INT:PBC ' lms2 <- modsem(tpb, TPB, method = \"lms\", nodes = 32) summary(lms2) #> Estimating null model #> EM: Iteration = 1, LogLik = -26393.22, Change = -26393.223 #> EM: Iteration = 2, LogLik = -26393.22, Change = 0.000 #> #> modsem (version 1.0.3): #> Estimator LMS #> Optimization method EM-NLMINB #> Number of observations 2000 #> Number of iterations 70 #> Loglikelihood -23439.02 #> Akaike (AIC) 46986.04 #> Bayesian (BIC) 47288.49 #> #> Numerical Integration: #> Points of integration (per dim) 32 #> Dimensions 1 #> Total points of integration 32 #> #> Fit Measures for H0: #> Loglikelihood -26393 #> Akaike (AIC) 52892.45 #> Bayesian (BIC) 53189.29 #> Chi-square 66.27 #> Degrees of Freedom (Chi-square) 82 #> P-value (Chi-square) 0.897 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 2954.20 #> Difference test (D) 5908.41 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> INT 0.364 #> BEH 0.259 #> R-Squared Null-Model (H0): #> INT 0.367 #> BEH 0.210 #> R-Squared Change: #> INT -0.003 #> BEH 0.049 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information expected #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> PBC =~ #> pbc1 1.000 #> pbc2 0.914 0.013 69.02 0.000 #> pbc3 0.802 0.012 65.40 0.000 #> ATT =~ #> att1 1.000 #> att2 0.878 0.012 70.82 0.000 #> att3 0.789 0.012 65.78 0.000 #> att4 0.695 0.011 61.10 0.000 #> att5 0.887 0.013 70.28 0.000 #> SN =~ #> sn1 1.000 #> sn2 0.889 0.017 52.14 0.000 #> INT =~ #> int1 1.000 #> int2 0.913 0.015 58.98 0.000 #> int3 0.807 0.014 55.84 0.000 #> BEH =~ #> b1 1.000 #> b2 0.959 0.030 31.77 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> INT ~ #> PBC 0.218 0.030 7.32 0.000 #> ATT 0.214 0.026 8.18 0.000 #> SN 0.176 0.027 6.42 0.000 #> BEH ~ #> PBC 0.233 0.023 10.24 0.000 #> INT 0.188 0.025 7.59 0.000 #> PBC:INT 0.205 0.019 11.04 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> pbc1 0.990 0.023 43.17 0.000 #> pbc2 0.978 0.021 45.79 0.000 #> pbc3 0.985 0.019 51.31 0.000 #> att1 1.009 0.024 41.46 0.000 #> att2 1.002 0.022 46.30 0.000 #> att3 1.012 0.020 51.24 0.000 #> att4 0.995 0.018 55.01 0.000 #> att5 0.988 0.022 44.94 0.000 #> sn1 1.001 0.024 40.93 0.000 #> sn2 1.006 0.022 46.05 0.000 #> int1 1.010 0.022 44.93 0.000 #> int2 1.009 0.021 48.14 0.000 #> int3 1.002 0.019 52.81 0.000 #> b1 0.999 0.022 45.57 0.000 #> b2 1.017 0.021 49.38 0.000 #> INT 0.000 #> BEH 0.000 #> PBC 0.000 #> ATT 0.000 #> SN 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> PBC ~~ #> ATT 0.668 0.021 31.56 0.000 #> SN 0.668 0.022 30.34 0.000 #> ATT ~~ #> SN 0.623 0.019 32.86 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> pbc1 0.148 0.008 18.92 0.000 #> pbc2 0.159 0.007 21.70 0.000 #> pbc3 0.155 0.007 23.70 0.000 #> att1 0.167 0.007 23.64 0.000 #> att2 0.150 0.006 24.73 0.000 #> att3 0.159 0.006 26.68 0.000 #> att4 0.162 0.006 27.71 0.000 #> att5 0.159 0.006 25.12 0.000 #> sn1 0.178 0.015 11.99 0.000 #> sn2 0.156 0.012 13.23 0.000 #> int1 0.157 0.009 18.36 0.000 #> int2 0.160 0.008 20.57 0.000 #> int3 0.168 0.007 24.33 0.000 #> b1 0.185 0.019 9.96 0.000 #> b2 0.136 0.017 8.13 0.000 #> PBC 0.947 0.017 54.56 0.000 #> ATT 0.992 0.014 69.78 0.000 #> SN 0.981 0.015 64.38 0.000 #> INT 0.491 0.020 25.00 0.000 #> BEH 0.456 0.023 20.13 0.000 qml2 <- modsem(tpb, TPB, method = \"qml\") summary(qml2, standardized = TRUE) # standardized estimates #> Estimating null model #> Starting M-step #> #> modsem (version 1.0.3): #> Estimator QML #> Optimization method NLMINB #> Number of observations 2000 #> Number of iterations 73 #> Loglikelihood -26326.25 #> Akaike (AIC) 52760.5 #> Bayesian (BIC) 53062.95 #> #> Fit Measures for H0: #> Loglikelihood -26393 #> Akaike (AIC) 52892.45 #> Bayesian (BIC) 53189.29 #> Chi-square 66.27 #> Degrees of Freedom (Chi-square) 82 #> P-value (Chi-square) 0.897 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 66.97 #> Difference test (D) 133.95 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> INT 0.366 #> BEH 0.263 #> R-Squared Null-Model (H0): #> INT 0.367 #> BEH 0.210 #> R-Squared Change: #> INT 0.000 #> BEH 0.053 #> #> Parameter Estimates: #> Coefficients standardized #> Information observed #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> PBC =~ #> pbc1 0.933 #> pbc2 0.913 0.013 69.47 0.000 #> pbc3 0.894 0.014 66.10 0.000 #> ATT =~ #> att1 0.925 #> att2 0.915 0.013 71.56 0.000 #> att3 0.892 0.013 66.38 0.000 #> att4 0.865 0.014 61.00 0.000 #> att5 0.912 0.013 70.85 0.000 #> SN =~ #> sn1 0.921 #> sn2 0.913 0.017 52.61 0.000 #> INT =~ #> int1 0.912 #> int2 0.895 0.015 59.05 0.000 #> int3 0.866 0.016 55.73 0.000 #> BEH =~ #> b1 0.877 #> b2 0.900 0.028 31.71 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> INT ~ #> PBC 0.243 0.033 7.35 0.000 #> ATT 0.242 0.030 8.16 0.000 #> SN 0.199 0.031 6.37 0.000 #> BEH ~ #> PBC 0.289 0.028 10.37 0.000 #> INT 0.212 0.028 7.69 0.000 #> PBC:INT 0.227 0.020 11.32 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> PBC ~~ #> ATT 0.692 0.030 23.45 0.000 #> SN 0.695 0.030 23.08 0.000 #> ATT ~~ #> SN 0.634 0.029 21.70 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> pbc1 0.130 0.007 18.39 0.000 #> pbc2 0.166 0.008 21.43 0.000 #> pbc3 0.201 0.008 23.89 0.000 #> att1 0.144 0.006 23.53 0.000 #> att2 0.164 0.007 24.71 0.000 #> att3 0.204 0.008 26.38 0.000 #> att4 0.252 0.009 27.65 0.000 #> att5 0.168 0.007 24.93 0.000 #> sn1 0.153 0.013 12.09 0.000 #> sn2 0.167 0.013 13.26 0.000 #> int1 0.168 0.009 18.11 0.000 #> int2 0.199 0.010 20.41 0.000 #> int3 0.249 0.011 23.55 0.000 #> b1 0.231 0.023 10.12 0.000 #> b2 0.191 0.024 8.10 0.000 #> PBC 1.000 0.037 27.07 0.000 #> ATT 1.000 0.037 26.93 0.000 #> SN 1.000 0.040 25.22 0.000 #> INT 0.634 0.026 24.64 0.000 #> BEH 0.737 0.037 20.17 0.000"},{"path":"/articles/modsem.html","id":"the-basic-syntax","dir":"Articles","previous_headings":"","what":"The Basic Syntax","title":"modsem","text":"modsem basically introduces new feature lavaan-syntax – semicolon operator (“:”). semicolon operator works way lm()-function. order specify interaction effect two variables, join Var1:Var2, Models can either estimated using one product indicator approaches (“ca”, “rca”, “dblcent”, “pind”) using latent moderated structural equations approach (“lms”), quasi maximum likelihood approach (“qml”). product indicator approaches estimated via lavaan, whilst lms qml approaches estimated via modsem .","code":""},{"path":"/articles/modsem.html","id":"a-simple-example","dir":"Articles","previous_headings":"The Basic Syntax","what":"A Simple Example","title":"modsem","text":"can see simple example specify interaction effect two latent variables lavaan. default model estimated using “dblcent” method. want use another method, method can changed using method argument.","code":"m1 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' est1 <- modsem(m1, oneInt) summary(est1) #> modsem: #> Method = dblcent #> lavaan 0.6-19 ended normally after 159 iterations #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 60 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 122.924 #> Degrees of freedom 111 #> P-value (Chi-square) 0.207 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Latent Variables: #> Estimate Std.Err z-value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.804 0.013 63.612 0.000 #> x3 0.916 0.014 67.144 0.000 #> Y =~ #> y1 1.000 #> y2 0.798 0.007 107.428 0.000 #> y3 0.899 0.008 112.453 0.000 #> Z =~ #> z1 1.000 #> z2 0.812 0.013 64.763 0.000 #> z3 0.882 0.013 67.014 0.000 #> XZ =~ #> x1z1 1.000 #> x2z1 0.805 0.013 60.636 0.000 #> x3z1 0.877 0.014 62.680 0.000 #> x1z2 0.793 0.013 59.343 0.000 #> x2z2 0.646 0.015 43.672 0.000 #> x3z2 0.706 0.016 44.292 0.000 #> x1z3 0.887 0.014 63.700 0.000 #> x2z3 0.716 0.016 45.645 0.000 #> x3z3 0.781 0.017 45.339 0.000 #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> Y ~ #> X 0.675 0.027 25.379 0.000 #> Z 0.561 0.026 21.606 0.000 #> XZ 0.702 0.027 26.360 0.000 #> #> Covariances: #> Estimate Std.Err z-value P(>|z|) #> .x1z1 ~~ #> .x2z2 0.000 #> .x2z3 0.000 #> .x3z2 0.000 #> .x3z3 0.000 #> .x2z1 ~~ #> .x1z2 0.000 #> .x1z2 ~~ #> .x2z3 0.000 #> .x3z1 ~~ #> .x1z2 0.000 #> .x1z2 ~~ #> .x3z3 0.000 #> .x2z1 ~~ #> .x1z3 0.000 #> .x2z2 ~~ #> .x1z3 0.000 #> .x3z1 ~~ #> .x1z3 0.000 #> .x3z2 ~~ #> .x1z3 0.000 #> .x2z1 ~~ #> .x3z2 0.000 #> .x3z3 0.000 #> .x3z1 ~~ #> .x2z2 0.000 #> .x2z2 ~~ #> .x3z3 0.000 #> .x3z1 ~~ #> .x2z3 0.000 #> .x3z2 ~~ #> .x2z3 0.000 #> .x1z1 ~~ #> .x1z2 0.115 0.008 14.802 0.000 #> .x1z3 0.114 0.008 13.947 0.000 #> .x2z1 0.125 0.008 16.095 0.000 #> .x3z1 0.140 0.009 16.135 0.000 #> .x1z2 ~~ #> .x1z3 0.103 0.007 14.675 0.000 #> .x2z2 0.128 0.006 20.850 0.000 #> .x3z2 0.146 0.007 21.243 0.000 #> .x1z3 ~~ #> .x2z3 0.116 0.007 17.818 0.000 #> .x3z3 0.135 0.007 18.335 0.000 #> .x2z1 ~~ #> .x2z2 0.135 0.006 20.905 0.000 #> .x2z3 0.145 0.007 21.145 0.000 #> .x3z1 0.114 0.007 16.058 0.000 #> .x2z2 ~~ #> .x2z3 0.117 0.006 20.419 0.000 #> .x3z2 0.116 0.006 20.586 0.000 #> .x2z3 ~~ #> .x3z3 0.109 0.006 18.059 0.000 #> .x3z1 ~~ #> .x3z2 0.138 0.007 19.331 0.000 #> .x3z3 0.158 0.008 20.269 0.000 #> .x3z2 ~~ #> .x3z3 0.131 0.007 19.958 0.000 #> X ~~ #> Z 0.201 0.024 8.271 0.000 #> XZ 0.016 0.025 0.628 0.530 #> Z ~~ #> XZ 0.062 0.025 2.449 0.014 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .x1 0.160 0.009 17.871 0.000 #> .x2 0.162 0.007 22.969 0.000 #> .x3 0.163 0.008 20.161 0.000 #> .y1 0.159 0.009 17.896 0.000 #> .y2 0.154 0.007 22.640 0.000 #> .y3 0.164 0.008 20.698 0.000 #> .z1 0.168 0.009 18.143 0.000 #> .z2 0.158 0.007 22.264 0.000 #> .z3 0.158 0.008 20.389 0.000 #> .x1z1 0.311 0.014 22.227 0.000 #> .x2z1 0.292 0.011 27.287 0.000 #> .x3z1 0.327 0.012 26.275 0.000 #> .x1z2 0.290 0.011 26.910 0.000 #> .x2z2 0.239 0.008 29.770 0.000 #> .x3z2 0.270 0.009 29.117 0.000 #> .x1z3 0.272 0.012 23.586 0.000 #> .x2z3 0.245 0.009 27.979 0.000 #> .x3z3 0.297 0.011 28.154 0.000 #> X 0.981 0.036 26.895 0.000 #> .Y 0.990 0.038 25.926 0.000 #> Z 1.016 0.038 26.856 0.000 #> XZ 1.045 0.044 24.004 0.000 est1 <- modsem(m1, oneInt, method = \"lms\") summary(est1) #> Estimating null model #> EM: Iteration = 1, LogLik = -17831.87, Change = -17831.875 #> EM: Iteration = 2, LogLik = -17831.87, Change = 0.000 #> #> modsem (version 1.0.3): #> Estimator LMS #> Optimization method EM-NLMINB #> Number of observations 2000 #> Number of iterations 92 #> Loglikelihood -14687.85 #> Akaike (AIC) 29437.71 #> Bayesian (BIC) 29611.34 #> #> Numerical Integration: #> Points of integration (per dim) 24 #> Dimensions 1 #> Total points of integration 24 #> #> Fit Measures for H0: #> Loglikelihood -17832 #> Akaike (AIC) 35723.75 #> Bayesian (BIC) 35891.78 #> Chi-square 17.52 #> Degrees of Freedom (Chi-square) 24 #> P-value (Chi-square) 0.826 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 3144.02 #> Difference test (D) 6288.04 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> Y 0.596 #> R-Squared Null-Model (H0): #> Y 0.395 #> R-Squared Change: #> Y 0.201 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information expected #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.804 0.012 65.27 0.000 #> x3 0.915 0.013 68.77 0.000 #> Z =~ #> z1 1.000 #> z2 0.810 0.012 65.55 0.000 #> z3 0.881 0.013 69.05 0.000 #> Y =~ #> y1 1.000 #> y2 0.799 0.008 106.30 0.000 #> y3 0.899 0.008 112.47 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> Y ~ #> X 0.676 0.032 20.89 0.000 #> Z 0.572 0.029 19.53 0.000 #> X:Z 0.712 0.027 26.72 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> x1 1.025 0.021 48.95 0.000 #> x2 1.218 0.018 68.87 0.000 #> x3 0.922 0.020 47.18 0.000 #> z1 1.016 0.028 36.17 0.000 #> z2 1.209 0.023 51.86 0.000 #> z3 0.920 0.025 36.75 0.000 #> y1 1.046 0.035 29.91 0.000 #> y2 1.227 0.029 42.98 0.000 #> y3 0.962 0.032 30.17 0.000 #> Y 0.000 #> X 0.000 #> Z 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> X ~~ #> Z 0.198 0.027 7.29 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> x1 0.160 0.008 19.63 0.000 #> x2 0.163 0.007 24.10 0.000 #> x3 0.165 0.008 21.53 0.000 #> z1 0.166 0.009 18.74 0.000 #> z2 0.160 0.007 22.64 0.000 #> z3 0.158 0.008 20.78 0.000 #> y1 0.160 0.009 17.98 0.000 #> y2 0.154 0.007 22.74 0.000 #> y3 0.163 0.008 20.73 0.000 #> X 0.972 0.016 60.80 0.000 #> Z 1.017 0.019 54.92 0.000 #> Y 0.984 0.036 27.12 0.000"},{"path":"/articles/modsem.html","id":"interactions-between-two-observed-variables","dir":"Articles","previous_headings":"The Basic Syntax","what":"Interactions Between two Observed Variables","title":"modsem","text":"modsem allow estimate interactions latent variables, also interactions observed variables. first run regression observed variables, interaction x1 z2, run equivalent model using modsem(). Regression Using modsem() general, interactions observed variables recommended use method = “pind”. Interaction effects observed variables supported LMS- QML-approach. certain circumstances, can define latent variabale single indicator estimate interaction effect two observed variables, LMS QML approach, generally recommended.","code":"reg1 <- lm(y1 ~ x1*z1, oneInt) summary(reg1) #> #> Call: #> lm(formula = y1 ~ x1 * z1, data = oneInt) #> #> Residuals: #> Min 1Q Median 3Q Max #> -3.7155 -0.8087 -0.0367 0.8078 4.6531 #> #> Coefficients: #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 0.51422 0.04618 11.135 <2e-16 *** #> x1 0.05477 0.03387 1.617 0.1060 #> z1 -0.06575 0.03461 -1.900 0.0576 . #> x1:z1 0.54361 0.02272 23.926 <2e-16 *** #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> #> Residual standard error: 1.184 on 1996 degrees of freedom #> Multiple R-squared: 0.4714, Adjusted R-squared: 0.4706 #> F-statistic: 593.3 on 3 and 1996 DF, p-value: < 2.2e-16 # Here we use \"pind\" as the method (see chapter 3) est2 <- modsem('y1 ~ x1 + z1 + x1:z1', data = oneInt, method = \"pind\") summary(est2) #> modsem: #> Method = pind #> lavaan 0.6-19 ended normally after 1 iteration #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 4 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 0.000 #> Degrees of freedom 0 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> y1 ~ #> x1 0.055 0.034 1.619 0.105 #> z1 -0.066 0.035 -1.902 0.057 #> x1z1 0.544 0.023 23.950 0.000 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .y1 1.399 0.044 31.623 0.000"},{"path":"/articles/modsem.html","id":"interactions-between-latent-and-observed-variables","dir":"Articles","previous_headings":"The Basic Syntax","what":"Interactions between Latent and Observed Variables","title":"modsem","text":"modsem also allows estimate interaction effects latent observed variables. , just join latent observed variable colon, e.g., ‘latent:observer’. interactions observed variables, generally recommended use method = “pind” estimating effect observed x latent","code":"m3 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 # Inner model Y ~ X + z1 + X:z1 ' est3 <- modsem(m3, oneInt, method = \"pind\") summary(est3) #> modsem: #> Method = pind #> lavaan 0.6-19 ended normally after 45 iterations #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 22 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 4468.171 #> Degrees of freedom 32 #> P-value (Chi-square) 0.000 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Latent Variables: #> Estimate Std.Err z-value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.803 0.013 63.697 0.000 #> x3 0.915 0.014 67.548 0.000 #> Y =~ #> y1 1.000 #> y2 0.798 0.007 115.375 0.000 #> y3 0.899 0.007 120.783 0.000 #> Xz1 =~ #> x1z1 1.000 #> x2z1 0.947 0.010 96.034 0.000 #> x3z1 0.902 0.009 99.512 0.000 #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> Y ~ #> X 0.021 0.034 0.614 0.540 #> z1 -0.185 0.023 -8.096 0.000 #> Xz1 0.646 0.017 37.126 0.000 #> #> Covariances: #> Estimate Std.Err z-value P(>|z|) #> X ~~ #> Xz1 1.243 0.055 22.523 0.000 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .x1 0.158 0.009 17.976 0.000 #> .x2 0.164 0.007 23.216 0.000 #> .x3 0.162 0.008 20.325 0.000 #> .y1 0.158 0.009 17.819 0.000 #> .y2 0.154 0.007 22.651 0.000 #> .y3 0.164 0.008 20.744 0.000 #> .x1z1 0.315 0.017 18.328 0.000 #> .x2z1 0.428 0.019 22.853 0.000 #> .x3z1 0.337 0.016 21.430 0.000 #> X 0.982 0.036 26.947 0.000 #> .Y 1.112 0.040 27.710 0.000 #> Xz1 3.965 0.136 29.217 0.000"},{"path":"/articles/modsem.html","id":"quadratic-effects","dir":"Articles","previous_headings":"The Basic Syntax","what":"Quadratic Effects","title":"modsem","text":"essence, quadratic effects just special case interaction effects. Thus modsem can also used estimate quadratic effects.","code":"m4 <- ' # Outer Model X =~ x1 + x2 + x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + Z:X + X:X ' est4 <- modsem(m4, oneInt, \"qml\") summary(est4) #> Estimating null model #> Starting M-step #> #> modsem (version 1.0.3): #> Estimator QML #> Optimization method NLMINB #> Number of observations 2000 #> Number of iterations 123 #> Loglikelihood -17496.2 #> Akaike (AIC) 35056.4 #> Bayesian (BIC) 35235.63 #> #> Fit Measures for H0: #> Loglikelihood -17832 #> Akaike (AIC) 35723.75 #> Bayesian (BIC) 35891.78 #> Chi-square 17.52 #> Degrees of Freedom (Chi-square) 24 #> P-value (Chi-square) 0.826 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 335.68 #> Difference test (D) 671.35 #> Degrees of freedom (D) 2 #> P-value (D) 0.000 #> #> R-Squared: #> Y 0.607 #> R-Squared Null-Model (H0): #> Y 0.395 #> R-Squared Change: #> Y 0.212 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information observed #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.803 0.013 63.961 0.000 #> x3 0.914 0.013 67.797 0.000 #> Z =~ #> z1 1.000 #> z2 0.810 0.012 65.124 0.000 #> z3 0.881 0.013 67.621 0.000 #> Y =~ #> y1 1.000 #> y2 0.798 0.007 107.567 0.000 #> y3 0.899 0.008 112.542 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> Y ~ #> X 0.674 0.032 20.888 0.000 #> Z 0.566 0.030 18.948 0.000 #> X:X -0.005 0.023 -0.207 0.836 #> X:Z 0.713 0.029 24.554 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> x1 1.023 0.024 42.894 0.000 #> x2 1.216 0.020 60.996 0.000 #> x3 0.919 0.022 41.484 0.000 #> z1 1.012 0.024 41.576 0.000 #> z2 1.206 0.020 59.271 0.000 #> z3 0.916 0.022 42.063 0.000 #> y1 1.042 0.038 27.684 0.000 #> y2 1.224 0.030 40.159 0.000 #> y3 0.958 0.034 28.101 0.000 #> Y 0.000 #> X 0.000 #> Z 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> X ~~ #> Z 0.200 0.024 8.239 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> x1 0.158 0.009 18.145 0.000 #> x2 0.162 0.007 23.188 0.000 #> x3 0.165 0.008 20.821 0.000 #> z1 0.166 0.009 18.341 0.000 #> z2 0.159 0.007 22.622 0.000 #> z3 0.158 0.008 20.714 0.000 #> y1 0.159 0.009 17.975 0.000 #> y2 0.154 0.007 22.670 0.000 #> y3 0.164 0.008 20.711 0.000 #> X 0.983 0.036 26.994 0.000 #> Z 1.019 0.038 26.951 0.000 #> Y 0.943 0.038 24.820 0.000"},{"path":"/articles/modsem.html","id":"more-complicated-examples","dir":"Articles","previous_headings":"The Basic Syntax","what":"More Complicated Examples","title":"modsem","text":"can see complicated example using model theory planned behaviour. example included two quadratic- one interaction effect, using included dataset jordan. dataset subset PISA 2006 dataset. Note: approaches work well, might quite slow depending number interaction effects (particularly LMS- constrained approach).","code":"tpb <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) INT ~ ATT + SN + PBC BEH ~ INT + PBC + INT:PBC ' # the double centering apporach est_tpb <- modsem(tpb, TPB) # using the lms approach est_tpb_lms <- modsem(tpb, TPB, method = \"lms\") #> Warning: It is recommended that you have at least 32 nodes for interaction #> effects between exogenous and endogenous variables in the lms approach 'nodes = #> 24' summary(est_tpb_lms) #> Estimating null model #> EM: Iteration = 1, LogLik = -26393.22, Change = -26393.223 #> EM: Iteration = 2, LogLik = -26393.22, Change = 0.000 #> #> modsem (version 1.0.3): #> Estimator LMS #> Optimization method EM-NLMINB #> Number of observations 2000 #> Number of iterations 103 #> Loglikelihood -23463.37 #> Akaike (AIC) 47034.74 #> Bayesian (BIC) 47337.19 #> #> Numerical Integration: #> Points of integration (per dim) 24 #> Dimensions 1 #> Total points of integration 24 #> #> Fit Measures for H0: #> Loglikelihood -26393 #> Akaike (AIC) 52892.45 #> Bayesian (BIC) 53189.29 #> Chi-square 66.27 #> Degrees of Freedom (Chi-square) 82 #> P-value (Chi-square) 0.897 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 2929.85 #> Difference test (D) 5859.70 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> INT 0.361 #> BEH 0.248 #> R-Squared Null-Model (H0): #> INT 0.367 #> BEH 0.210 #> R-Squared Change: #> INT -0.006 #> BEH 0.038 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information expected #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> PBC =~ #> pbc1 1.000 #> pbc2 0.911 0.013 67.91 0.000 #> pbc3 0.802 0.012 65.67 0.000 #> ATT =~ #> att1 1.000 #> att2 0.877 0.012 71.32 0.000 #> att3 0.789 0.012 65.69 0.000 #> att4 0.695 0.011 60.84 0.000 #> att5 0.887 0.013 70.49 0.000 #> SN =~ #> sn1 1.000 #> sn2 0.889 0.017 51.79 0.000 #> INT =~ #> int1 1.000 #> int2 0.913 0.015 59.42 0.000 #> int3 0.807 0.014 55.75 0.000 #> BEH =~ #> b1 1.000 #> b2 0.961 0.030 31.82 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> INT ~ #> PBC 0.217 0.030 7.29 0.000 #> ATT 0.213 0.026 8.28 0.000 #> SN 0.177 0.028 6.34 0.000 #> BEH ~ #> PBC 0.228 0.023 10.06 0.000 #> INT 0.182 0.025 7.37 0.000 #> PBC:INT 0.204 0.019 10.98 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> pbc1 0.959 0.019 50.31 0.000 #> pbc2 0.950 0.018 53.08 0.000 #> pbc3 0.960 0.016 59.11 0.000 #> att1 0.987 0.022 44.10 0.000 #> att2 0.983 0.020 49.45 0.000 #> att3 0.995 0.018 54.27 0.000 #> att4 0.980 0.017 58.41 0.000 #> att5 0.969 0.020 48.14 0.000 #> sn1 0.979 0.023 43.04 0.000 #> sn2 0.987 0.020 48.23 0.000 #> int1 0.995 0.022 46.17 0.000 #> int2 0.995 0.020 49.49 0.000 #> int3 0.990 0.018 53.60 0.000 #> b1 0.989 0.022 45.86 0.000 #> b2 1.008 0.020 50.01 0.000 #> INT 0.000 #> BEH 0.000 #> PBC 0.000 #> ATT 0.000 #> SN 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> PBC ~~ #> ATT 0.658 0.020 32.31 0.000 #> SN 0.657 0.021 30.92 0.000 #> ATT ~~ #> SN 0.616 0.019 32.92 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> pbc1 0.147 0.008 19.39 0.000 #> pbc2 0.164 0.007 22.22 0.000 #> pbc3 0.154 0.006 24.15 0.000 #> att1 0.167 0.007 23.38 0.000 #> att2 0.150 0.006 24.30 0.000 #> att3 0.159 0.006 26.67 0.000 #> att4 0.163 0.006 27.66 0.000 #> att5 0.159 0.006 24.78 0.000 #> sn1 0.178 0.015 12.12 0.000 #> sn2 0.156 0.012 13.00 0.000 #> int1 0.157 0.009 18.18 0.000 #> int2 0.160 0.008 20.21 0.000 #> int3 0.168 0.007 23.39 0.000 #> b1 0.186 0.019 10.00 0.000 #> b2 0.135 0.017 8.03 0.000 #> PBC 0.933 0.015 60.19 0.000 #> ATT 0.985 0.014 70.17 0.000 #> SN 0.974 0.015 63.87 0.000 #> INT 0.491 0.020 24.40 0.000 #> BEH 0.456 0.022 20.28 0.000 m2 <- ' ENJ =~ enjoy1 + enjoy2 + enjoy3 + enjoy4 + enjoy5 CAREER =~ career1 + career2 + career3 + career4 SC =~ academic1 + academic2 + academic3 + academic4 + academic5 + academic6 CAREER ~ ENJ + SC + ENJ:ENJ + SC:SC + ENJ:SC ' est_jordan <- modsem(m2, data = jordan) est_jordan_qml <- modsem(m2, data = jordan, method = \"qml\") summary(est_jordan_qml) #> Estimating null model #> Starting M-step #> #> modsem (version 1.0.3): #> Estimator QML #> Optimization method NLMINB #> Number of observations 6038 #> Number of iterations 101 #> Loglikelihood -110520.22 #> Akaike (AIC) 221142.45 #> Bayesian (BIC) 221484.44 #> #> Fit Measures for H0: #> Loglikelihood -110521 #> Akaike (AIC) 221138.58 #> Bayesian (BIC) 221460.46 #> Chi-square 1016.34 #> Degrees of Freedom (Chi-square) 87 #> P-value (Chi-square) 0.000 #> RMSEA 0.005 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 1.07 #> Difference test (D) 2.13 #> Degrees of freedom (D) 3 #> P-value (D) 0.546 #> #> R-Squared: #> CAREER 0.512 #> R-Squared Null-Model (H0): #> CAREER 0.510 #> R-Squared Change: #> CAREER 0.002 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information observed #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> ENJ =~ #> enjoy1 1.000 #> enjoy2 1.002 0.020 50.587 0.000 #> enjoy3 0.894 0.020 43.669 0.000 #> enjoy4 0.999 0.021 48.227 0.000 #> enjoy5 1.047 0.021 50.400 0.000 #> SC =~ #> academic1 1.000 #> academic2 1.104 0.028 38.946 0.000 #> academic3 1.235 0.030 41.720 0.000 #> academic4 1.254 0.030 41.828 0.000 #> academic5 1.113 0.029 38.647 0.000 #> academic6 1.198 0.030 40.356 0.000 #> CAREER =~ #> career1 1.000 #> career2 1.040 0.016 65.180 0.000 #> career3 0.952 0.016 57.838 0.000 #> career4 0.818 0.017 48.358 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> CAREER ~ #> ENJ 0.523 0.020 26.286 0.000 #> SC 0.467 0.023 19.884 0.000 #> ENJ:ENJ 0.026 0.022 1.206 0.228 #> ENJ:SC -0.039 0.046 -0.851 0.395 #> SC:SC -0.002 0.035 -0.058 0.953 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> enjoy1 0.000 0.013 -0.008 0.994 #> enjoy2 0.000 0.015 0.010 0.992 #> enjoy3 0.000 0.013 -0.023 0.982 #> enjoy4 0.000 0.014 0.008 0.993 #> enjoy5 0.000 0.014 0.025 0.980 #> academic1 0.000 0.016 -0.009 0.993 #> academic2 0.000 0.014 -0.009 0.993 #> academic3 0.000 0.015 -0.028 0.978 #> academic4 0.000 0.016 -0.015 0.988 #> academic5 -0.001 0.014 -0.044 0.965 #> academic6 0.001 0.015 0.048 0.962 #> career1 -0.004 0.017 -0.204 0.838 #> career2 -0.004 0.018 -0.248 0.804 #> career3 -0.004 0.017 -0.214 0.830 #> career4 -0.004 0.016 -0.232 0.816 #> CAREER 0.000 #> ENJ 0.000 #> SC 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> ENJ ~~ #> SC 0.218 0.009 25.477 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> enjoy1 0.487 0.011 44.335 0.000 #> enjoy2 0.488 0.011 44.406 0.000 #> enjoy3 0.596 0.012 48.233 0.000 #> enjoy4 0.488 0.011 44.561 0.000 #> enjoy5 0.442 0.010 42.470 0.000 #> academic1 0.645 0.013 49.813 0.000 #> academic2 0.566 0.012 47.864 0.000 #> academic3 0.473 0.011 44.319 0.000 #> academic4 0.455 0.010 43.579 0.000 #> academic5 0.565 0.012 47.695 0.000 #> academic6 0.502 0.011 45.434 0.000 #> career1 0.373 0.009 40.392 0.000 #> career2 0.328 0.009 37.019 0.000 #> career3 0.436 0.010 43.272 0.000 #> career4 0.576 0.012 48.372 0.000 #> ENJ 0.500 0.017 29.547 0.000 #> SC 0.338 0.015 23.195 0.000 #> CAREER 0.302 0.010 29.711 0.000"},{"path":"/articles/observed_lms_qml.html","id":"the-latent-moderated-structural-equations-lms-and-the-quasi-maximum-likelihood-qml-approach","dir":"Articles","previous_headings":"","what":"The Latent Moderated Structural Equations (LMS) and the Quasi Maximum Likelihood (QML) approach","title":"observed variables in the LMS- and QML approach","text":"contrast approaches, LMS QML approaches designed handle latent variables . Thus observed variables easily used, approaches. One way getting around specifying observed variable latent variable single indicator. modsem() default constrain factor loading 1, residual variance indicator 0. , difference latent variable indicator, (assuming exogenous variable) zero-mean. work LMS- QML approach cases, except two exceptions.","code":""},{"path":"/articles/observed_lms_qml.html","id":"the-lms-approach","dir":"Articles","previous_headings":"The Latent Moderated Structural Equations (LMS) and the Quasi Maximum Likelihood (QML) approach","what":"The LMS approach","title":"observed variables in the LMS- and QML approach","text":"LMS approach can use mentioned approach almost cases, except case wish use observed variable moderating variable. LMS approach, usually select one variable interaction term moderator. interaction effect estimated via numerical integration, n quadrature nodes moderating variable. process however, requires moderating variable error-term, distribution moderating variable modelled X∼N(Az,ε)X \\sim N(Az, \\varepsilon), AzAz expected value XX quadrature point k, ε\\varepsilon error term. error-term zero, probability observing given value XX computable. instances first variable interaction term, chosen moderator. example, interaction term \"X:Z\", \"X\" usually chosen moderator. Thus one variables latent, put latent variable first interaction term. observed, specify measurement error (e.g., “x1 ~~ 0.1 * x1”) indicator first variable interaction term.","code":"library(modsem) # interaction effect between a latent and an observed variable m1 <- ' # Outer Model X =~ x1 # X is observed Z =~ z1 + z2 # Z is latent Y =~ y1 # Y is observed # Inner model Y ~ X + Z Y ~ Z:X ' lms1 <- modsem(m1, oneInt, method = \"lms\") # interaction effect between two observed variables m2 <- ' # Outer Model X =~ x1 # X is observed Z =~ z1 # Z is observed Y =~ y1 # Y is observed x1 ~~ 0.1 * x1 # specify a variance for the measurement error # Inner model Y ~ X + Z Y ~ X:Z ' lms2 <- modsem(m1, oneInt, method = \"lms\") summary(lms2) #> Estimating null model #> EM: Iteration = 1, LogLik = -10816.13, Change = -10816.126 #> EM: Iteration = 2, LogLik = -10816.13, Change = 0.000 #> #> modsem (version 1.0.3): #> Estimator LMS #> Optimization method EM-NLMINB #> Number of observations 2000 #> Number of iterations 58 #> Loglikelihood -8087.2 #> Akaike (AIC) 16202.4 #> Bayesian (BIC) 16280.81 #> #> Numerical Integration: #> Points of integration (per dim) 24 #> Dimensions 1 #> Total points of integration 24 #> #> Fit Measures for H0: #> Loglikelihood -10816 #> Akaike (AIC) 21658.25 #> Bayesian (BIC) 21731.06 #> Chi-square 0.01 #> Degrees of Freedom (Chi-square) 1 #> P-value (Chi-square) 0.917 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 2728.93 #> Difference test (D) 5457.85 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> Y 0.510 #> R-Squared Null-Model (H0): #> Y 0.343 #> R-Squared Change: #> Y 0.167 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information expected #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> Z =~ #> z1 1.000 #> z2 0.811 0.016 50.04 0.000 #> X =~ #> x1 1.000 #> Y =~ #> y1 1.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> Y ~ #> Z 0.587 0.033 17.65 0.000 #> X 0.574 0.030 19.03 0.000 #> Z:X 0.627 0.026 24.18 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> z1 1.009 0.027 37.84 0.000 #> z2 1.203 0.022 54.45 0.000 #> x1 1.023 0.027 38.49 0.000 #> y1 1.046 0.037 28.54 0.000 #> Y 0.000 #> Z 0.000 #> X 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> Z ~~ #> X 0.211 0.028 7.66 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> z1 0.170 0.017 10.24 0.000 #> z2 0.160 0.011 13.94 0.000 #> x1 0.000 #> y1 0.000 #> Z 1.010 0.020 51.26 0.000 #> X 1.141 0.017 69.00 0.000 #> Y 1.284 0.043 30.19 0.000"},{"path":"/articles/observed_lms_qml.html","id":"the-qml-approach","dir":"Articles","previous_headings":"The Latent Moderated Structural Equations (LMS) and the Quasi Maximum Likelihood (QML) approach","what":"The QML approach","title":"observed variables in the LMS- and QML approach","text":"estimation QML approach different LMS approach, issue LMS approach. Thus don’t specify measurement error moderating variables.","code":"m3 <- ' # Outer Model X =~ x1 # X is observed Z =~ z1 # Z is observed Y =~ y1 # Y is observed # Inner model Y ~ X + Z Y ~ X:Z ' qml3 <- modsem(m3, oneInt, method = \"qml\") summary(qml3) #> Estimating null model #> Starting M-step #> #> modsem (version 1.0.3): #> Estimator QML #> Optimization method NLMINB #> Number of observations 2000 #> Number of iterations 11 #> Loglikelihood -9117.07 #> Akaike (AIC) 18254.13 #> Bayesian (BIC) 18310.14 #> #> Fit Measures for H0: #> Loglikelihood -9369 #> Akaike (AIC) 18756.46 #> Bayesian (BIC) 18806.87 #> Chi-square 0.00 #> Degrees of Freedom (Chi-square) 0 #> P-value (Chi-square) 0.000 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 252.17 #> Difference test (D) 504.33 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> Y 0.470 #> R-Squared Null-Model (H0): #> Y 0.320 #> R-Squared Change: #> Y 0.150 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information observed #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> X =~ #> x1 1.000 #> Z =~ #> z1 1.000 #> Y =~ #> y1 1.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> Y ~ #> X 0.605 0.028 21.26 0.000 #> Z 0.490 0.028 17.55 0.000 #> X:Z 0.544 0.023 23.95 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> x1 1.023 0.024 42.83 0.000 #> z1 1.011 0.024 41.56 0.000 #> y1 1.066 0.034 31.64 0.000 #> Y 0.000 #> X 0.000 #> Z 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> X ~~ #> Z 0.210 0.026 7.95 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> x1 0.000 #> z1 0.000 #> y1 0.000 #> X 1.141 0.036 31.62 0.000 #> Z 1.184 0.037 31.62 0.000 #> Y 1.399 0.044 31.62 0.000"},{"path":"/articles/plot_interactions.html","id":"plotting-interaction-effects","dir":"Articles","previous_headings":"","what":"Plotting interaction effects","title":"plotting interaction effects","text":"Interaction effects can plotted using included plot_interaction function. function takes fitted model object names two variables interacting. function plot interaction effect two variables. x-variable plotted x-axis y-variable plotted y-axis. z-variable decides points z effect x y plotted. function also plot 95% confidence interval interaction effect. can see simple example using double centering approach. can see different example using LMS approach, theory planned behavior model.","code":"m1 <- \" # Outer Model X =~ x1 X =~ x2 + x3 Z =~ z1 + z2 + z3 Y =~ y1 + y2 + y3 # Inner model Y ~ X + Z + X:Z \" est1 <- modsem(m1, data = oneInt) plot_interaction(\"X\", \"Z\", \"Y\", \"X:Z\", -3:3, c(-0.2, 0), est1) tpb <- \" # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ PBC:INT \" est2 <- modsem(tpb, TPB, method = \"lms\") #> Warning: It is recommended that you have at least 32 nodes for interaction #> effects between exogenous and endogenous variables in the lms approach 'nodes = #> 24' plot_interaction(x = \"INT\", z = \"PBC\", y = \"BEH\", xz = \"PBC:INT\", vals_z = c(-0.5, 0.5), model = est2)"},{"path":"/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Kjell Solem Slupphaug. Author, maintainer.","code":""},{"path":"/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Slupphaug, K. S., Mehmetoglu, M., & Mittner, M. (2024). modsem: R package estimating latent interactions quadratic effects. Structural Equation Modeling: Multidisciplinary Journal doi:10.1080/10705511.2024.2417409","code":"@Article{, title = {modsem: An R package for estimating latent interactions and quadratic effects}, author = {Kjell Solem Slupphaug and Mehmet Mehmetoglu and Matthias Mittner}, journal = {Structural Equation Modeling: A Multidisciplinary Journal}, year = {2024}, doi = {10.1080/10705511.2024.2417409}, }"},{"path":"/index.html","id":"modsem-","dir":"","previous_headings":"","what":"Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)","title":"Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)","text":"package allows perform interactions latent variables (.e., moderation) CB-SEM. See https://kss2k.github.io/modsem/ tutorial.","code":""},{"path":"/index.html","id":"to-install","dir":"","previous_headings":"","what":"To Install","title":"Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)","text":"","code":"# From CRAN install.packages(\"modsem\") # Latest version from Github install.packages(\"devtools\") devtools::install_github(\"kss2k/modsem\", build_vignettes = TRUE)"},{"path":"/index.html","id":"methodsapproaches","dir":"","previous_headings":"","what":"Methods/Approaches","title":"Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)","text":"number approaches estimating interaction effects SEM. modsem(), method = \"method\" argument allows choose use. Note constraints can become quite complicated complex models, particularly interaction including enodgenous variables. method can therefore quite slow. \"uca\" = unconstrained approach (Marsh, 2004) \"rca\" = residual centering approach (Little et al., 2006) default \"pind\" = basic product indicator approach (recommended) \"lms\" = Latent Moderated Structural equations (LMS) approach, see vignette \"qml\" = Quasi Maximum Likelihood (QML) approach, see vignette estimates model Mplus, installed","code":""},{"path":[]},{"path":"/index.html","id":"one-interaction","dir":"","previous_headings":"","what":"One interaction","title":"Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)","text":"","code":"library(modsem) m1 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' # Double centering approach est1_dca <- modsem(m1, oneInt) summary(est1_dca) # Constrained approach est1_ca <- modsem(m1, oneInt, method = \"ca\") summary(est1_ca) # QML approach est1_qml <- modsem(m1, oneInt, method = \"qml\") summary(est1_qml, standardized = TRUE) # LMS approach est1_lms <- modsem(m1, oneInt, method = \"lms\") summary(est1_lms)"},{"path":"/index.html","id":"theory-of-planned-behavior","dir":"","previous_headings":"","what":"Theory Of Planned Behavior","title":"Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)","text":"","code":"tpb <- \" # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) # Causal Relationsships INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ PBC:INT \" # double centering approach est_tpb_dca <- modsem(tpb, data = TPB, method = \"dblcent\") summary(est_tpb_dca) # Constrained approach using Wrigths path tracing rules for generating # the appropriate constraints est_tpb_ca <- modsem(tpb, data = TPB, method = \"ca\") summary(est_tpb_ca) # LMS approach est_tpb_lms <- modsem(tpb, data = TPB, method = \"lms\") summary(est_tpb_lms, standardized = TRUE) # QML approach est_tpb_qml <- modsem(tpb, data = TPB, method = \"qml\") summary(est_tpb_qml, standardized = TRUE)"},{"path":"/index.html","id":"interactions-between-two-observed-variables","dir":"","previous_headings":"","what":"Interactions between two observed variables","title":"Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)","text":"","code":"est2 <- modsem('y1 ~ x1 + z1 + x1:z1', data = oneInt, method = \"pind\") summary(est2) ## Interaction between an obsereved and a latent variable m3 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 # Inner model Y ~ X + z1 + X:z1 ' est3 <- modsem(m3, oneInt, method = \"pind\") summary(est3)"},{"path":"/reference/TPB.html","id":null,"dir":"Reference","previous_headings":"","what":"TPB — TPB","title":"TPB — TPB","text":"simulated dataset based Theory Planned Behaviour","code":""},{"path":"/reference/TPB.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"TPB — TPB","text":"","code":"tpb <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) INT ~ ATT + SN + PBC BEH ~ INT + PBC + INT:PBC ' est <- modsem(tpb, data = TPB)"},{"path":"/reference/TPB_UK.html","id":null,"dir":"Reference","previous_headings":"","what":"TPB_UK — TPB_UK","title":"TPB_UK — TPB_UK","text":"dataset based Theory Planned Behaviour UK sample. 4 variables high communality selected latent variable (ATT, SN, PBC, INT, BEH), two time points (t1 t2).","code":""},{"path":"/reference/TPB_UK.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"TPB_UK — TPB_UK","text":"Gathered replciation study original Hagger et al. (2023). Obtained https://doi.org/10.23668/psycharchives.12187","code":""},{"path":"/reference/TPB_UK.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"TPB_UK — TPB_UK","text":"","code":"tpb_uk <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att3 + att2 + att1 + att4 SN =~ sn4 + sn2 + sn3 + sn1 PBC =~ pbc2 + pbc1 + pbc3 + pbc4 INT =~ int2 + int1 + int3 + int4 BEH =~ beh3 + beh2 + beh1 + beh4 # Inner Model (Based on Steinmetz et al., 2011) # Causal Relationsships INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ INT:PBC ' est <- modsem(tpb_uk, data = TPB_UK)"},{"path":"/reference/coef_modsem_da.html","id":null,"dir":"Reference","previous_headings":"","what":"Wrapper for coef — coef_modsem_da","title":"Wrapper for coef — coef_modsem_da","text":"wrapper coef, used modsem::coef_modsem_da, since coef namespace modsem, stats","code":""},{"path":"/reference/coef_modsem_da.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Wrapper for coef — coef_modsem_da","text":"","code":"coef_modsem_da(object, ...)"},{"path":"/reference/coef_modsem_da.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Wrapper for coef — coef_modsem_da","text":"object fittet model inspect ... additional arguments","code":""},{"path":"/reference/compare_fit.html","id":null,"dir":"Reference","previous_headings":"","what":"compare model fit for qml and lms models — compare_fit","title":"compare model fit for qml and lms models — compare_fit","text":"Compare fit two models using likelihood ratio test. `estH0` representing null hypothesis model, `estH1` alternative hypothesis model. Importantly, function assumes `estH0` free parameters (.e., degrees freedom) `estH1`. alternative hypothesis model","code":""},{"path":"/reference/compare_fit.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"compare model fit for qml and lms models — compare_fit","text":"","code":"compare_fit(estH0, estH1)"},{"path":"/reference/compare_fit.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"compare model fit for qml and lms models — compare_fit","text":"estH0 object class `modsem_da` representing null hypothesis model estH1 object class `modsem_da` representing ","code":""},{"path":"/reference/compare_fit.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"compare model fit for qml and lms models — compare_fit","text":"","code":"if (FALSE) { # \\dontrun{ H0 <- \" # Outer Model X =~ x1 + x2 + x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z \" estH0 <- modsem(m1, oneInt, \"lms\") H1 <- \" # Outer Model X =~ x1 + x2 + x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z \" estH1 <- modsem(m1, oneInt, \"lms\") compare_fit(estH0, estH1) } # }"},{"path":"/reference/default_settings_da.html","id":null,"dir":"Reference","previous_headings":"","what":"default arguments fro LMS and QML approach — default_settings_da","title":"default arguments fro LMS and QML approach — default_settings_da","text":"function returns default settings LMS QML approach.","code":""},{"path":"/reference/default_settings_da.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"default arguments fro LMS and QML approach — default_settings_da","text":"","code":"default_settings_da(method = c(\"lms\", \"qml\"))"},{"path":"/reference/default_settings_da.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"default arguments fro LMS and QML approach — default_settings_da","text":"method method get settings ","code":""},{"path":"/reference/default_settings_da.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"default arguments fro LMS and QML approach — default_settings_da","text":"list","code":""},{"path":"/reference/default_settings_da.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"default arguments fro LMS and QML approach — default_settings_da","text":"","code":"library(modsem) default_settings_da() #> $lms #> $lms$verbose #> [1] FALSE #> #> $lms$optimize #> [1] TRUE #> #> $lms$nodes #> [1] 24 #> #> $lms$convergence #> [1] 1e-04 #> #> $lms$optimizer #> [1] \"nlminb\" #> #> $lms$center.data #> [1] FALSE #> #> $lms$standardize.data #> [1] FALSE #> #> $lms$standardize.out #> [1] FALSE #> #> $lms$standardize #> [1] FALSE #> #> $lms$mean.observed #> [1] TRUE #> #> $lms$double #> [1] FALSE #> #> $lms$calc.se #> [1] TRUE #> #> $lms$FIM #> [1] \"expected\" #> #> $lms$OFIM.hessian #> [1] FALSE #> #> $lms$EFIM.S #> [1] 30000 #> #> $lms$EFIM.parametric #> [1] TRUE #> #> $lms$robust.se #> [1] FALSE #> #> $lms$max.iter #> [1] 500 #> #> $lms$max.step #> [1] 1 #> #> $lms$fix.estep #> [1] TRUE #> #> $lms$epsilon #> [1] 1e-04 #> #> $lms$quad.range #> [1] Inf #> #> $lms$n.threads #> NULL #> #> #> $qml #> $qml$verbose #> [1] FALSE #> #> $qml$optimize #> [1] TRUE #> #> $qml$nodes #> [1] 0 #> #> $qml$convergence #> [1] 1e-06 #> #> $qml$optimizer #> [1] \"nlminb\" #> #> $qml$center.data #> [1] FALSE #> #> $qml$standardize #> [1] FALSE #> #> $qml$standardize.data #> [1] FALSE #> #> $qml$standardize.out #> [1] FALSE #> #> $qml$mean.observed #> [1] TRUE #> #> $qml$double #> [1] FALSE #> #> $qml$calc.se #> [1] TRUE #> #> $qml$FIM #> [1] \"observed\" #> #> $qml$OFIM.hessian #> [1] TRUE #> #> $qml$EFIM.S #> [1] 30000 #> #> $qml$EFIM.parametric #> [1] TRUE #> #> $qml$robust.se #> [1] FALSE #> #> $qml$max.iter #> [1] 500 #> #> $qml$max.step #> NULL #> #> $qml$fix.estep #> NULL #> #> $qml$epsilon #> [1] 1e-08 #> #> $qml$quad.range #> [1] Inf #> #> $qml$n.threads #> NULL #> #>"},{"path":"/reference/default_settings_pi.html","id":null,"dir":"Reference","previous_headings":"","what":"default arguments for product indicator approaches — default_settings_pi","title":"default arguments for product indicator approaches — default_settings_pi","text":"function returns default settings product indicator approaches","code":""},{"path":"/reference/default_settings_pi.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"default arguments for product indicator approaches — default_settings_pi","text":"","code":"default_settings_pi(method = c(\"rca\", \"uca\", \"pind\", \"dblcent\", \"ca\"))"},{"path":"/reference/default_settings_pi.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"default arguments for product indicator approaches — default_settings_pi","text":"method method get settings ","code":""},{"path":"/reference/default_settings_pi.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"default arguments for product indicator approaches — default_settings_pi","text":"list","code":""},{"path":"/reference/default_settings_pi.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"default arguments for product indicator approaches — default_settings_pi","text":"","code":"library(modsem) default_settings_pi() #> $rca #> $rca$center.before #> [1] FALSE #> #> $rca$center.after #> [1] FALSE #> #> $rca$residuals.prods #> [1] TRUE #> #> $rca$residual.cov.syntax #> [1] TRUE #> #> $rca$constrained.prod.mean #> [1] FALSE #> #> $rca$constrained.loadings #> [1] FALSE #> #> $rca$constrained.var #> [1] FALSE #> #> $rca$constrained.res.cov.method #> [1] \"simple\" #> #> $rca$match #> [1] FALSE #> #> #> $uca #> $uca$center.before #> [1] TRUE #> #> $uca$center.after #> [1] FALSE #> #> $uca$residuals.prods #> [1] FALSE #> #> $uca$residual.cov.syntax #> [1] TRUE #> #> $uca$constrained.prod.mean #> [1] TRUE #> #> $uca$constrained.loadings #> [1] FALSE #> #> $uca$constrained.var #> [1] FALSE #> #> $uca$constrained.res.cov.method #> [1] \"simple\" #> #> $uca$match #> [1] FALSE #> #> #> $pind #> $pind$center.before #> [1] FALSE #> #> $pind$center.after #> [1] FALSE #> #> $pind$residuals.prods #> [1] FALSE #> #> $pind$residual.cov.syntax #> [1] FALSE #> #> $pind$constrained.prod.mean #> [1] FALSE #> #> $pind$constrained.loadings #> [1] FALSE #> #> $pind$constrained.var #> [1] FALSE #> #> $pind$constrained.res.cov.method #> [1] \"simple\" #> #> $pind$match #> [1] FALSE #> #> #> $dblcent #> $dblcent$center.before #> [1] TRUE #> #> $dblcent$center.after #> [1] TRUE #> #> $dblcent$residuals.prods #> [1] FALSE #> #> $dblcent$residual.cov.syntax #> [1] TRUE #> #> $dblcent$constrained.prod.mean #> [1] FALSE #> #> $dblcent$constrained.loadings #> [1] FALSE #> #> $dblcent$constrained.var #> [1] FALSE #> #> $dblcent$constrained.res.cov.method #> [1] \"simple\" #> #> $dblcent$match #> [1] FALSE #> #> #> $ca #> $ca$center.before #> [1] TRUE #> #> $ca$center.after #> [1] FALSE #> #> $ca$residuals.prods #> [1] FALSE #> #> $ca$residual.cov.syntax #> [1] TRUE #> #> $ca$constrained.prod.mean #> [1] TRUE #> #> $ca$constrained.loadings #> [1] TRUE #> #> $ca$constrained.var #> [1] TRUE #> #> $ca$constrained.res.cov.method #> [1] \"ca\" #> #> $ca$match #> [1] TRUE #> #>"},{"path":"/reference/extract_lavaan.html","id":null,"dir":"Reference","previous_headings":"","what":"extract lavaan object from modsem object estimated using product indicators — extract_lavaan","title":"extract lavaan object from modsem object estimated using product indicators — extract_lavaan","text":"extract lavaan object modsem object estimated using product indicators","code":""},{"path":"/reference/extract_lavaan.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"extract lavaan object from modsem object estimated using product indicators — extract_lavaan","text":"","code":"extract_lavaan(object)"},{"path":"/reference/extract_lavaan.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"extract lavaan object from modsem object estimated using product indicators — extract_lavaan","text":"object modsem object","code":""},{"path":"/reference/extract_lavaan.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"extract lavaan object from modsem object estimated using product indicators — extract_lavaan","text":"lavaan object","code":""},{"path":"/reference/extract_lavaan.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"extract lavaan object from modsem object estimated using product indicators — extract_lavaan","text":"","code":"library(modsem) m1 <- ' # Outer Model X =~ x1 + x2 + x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' est <- modsem_pi(m1, oneInt) lav_est <- extract_lavaan(est)"},{"path":"/reference/fit_modsem_da.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit measures for QML and LMS models — fit_modsem_da","title":"Fit measures for QML and LMS models — fit_modsem_da","text":"Calculates chi-sq test p-value, well RMSEA LMS QML models. Note Chi-Square based fit measures calculated baseline model, .e., model without interaction effect","code":""},{"path":"/reference/fit_modsem_da.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit measures for QML and LMS models — fit_modsem_da","text":"","code":"fit_modsem_da(model, chisq = TRUE)"},{"path":"/reference/fit_modsem_da.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit measures for QML and LMS models — fit_modsem_da","text":"model fitted model. Thereafter, can use 'compare_fit()' assess comparative fit models. interaction effect makes model better, e.g., RMSEA good baseline model, interaction model likely good RMSEA well. chisq Chi-Square based fit-measures calculated?","code":""},{"path":"/reference/get_pi_data.html","id":null,"dir":"Reference","previous_headings":"","what":"Get data with product indicators for different approaches — get_pi_data","title":"Get data with product indicators for different approaches — get_pi_data","text":"get_pi_syntax() function creating lavaan syntax used estimating latent interaction models using one product indicators lavaan.","code":""},{"path":"/reference/get_pi_data.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get data with product indicators for different approaches — get_pi_data","text":"","code":"get_pi_data(model.syntax, data, method = \"dblcent\", match = FALSE, ...)"},{"path":"/reference/get_pi_data.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get data with product indicators for different approaches — get_pi_data","text":"model.syntax lavaan syntax data data create product indicators method method use: \"rca\" = residual centering approach, \"uca\" = unconstrained approach, \"dblcent\" = double centering approach, \"pind\" = prod ind approach, constraints centering, \"custom\" = use parameters specified function call match product indicators created using match-strategy ... arguments passed functions (e.g., modsem_pi)","code":""},{"path":"/reference/get_pi_data.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get data with product indicators for different approaches — get_pi_data","text":"data.frame","code":""},{"path":"/reference/get_pi_data.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Get data with product indicators for different approaches — get_pi_data","text":"","code":"library(modsem) library(lavaan) #> This is lavaan 0.6-19 #> lavaan is FREE software! Please report any bugs. m1 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' syntax <- get_pi_syntax(m1) data <- get_pi_data(m1, oneInt) est <- sem(syntax, data)"},{"path":"/reference/get_pi_syntax.html","id":null,"dir":"Reference","previous_headings":"","what":"Get lavaan syntax for product indicator approaches — get_pi_syntax","title":"Get lavaan syntax for product indicator approaches — get_pi_syntax","text":"get_pi_syntax() function creating lavaan syntax used estimating latent interaction models using one product indicators lavaan.","code":""},{"path":"/reference/get_pi_syntax.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get lavaan syntax for product indicator approaches — get_pi_syntax","text":"","code":"get_pi_syntax(model.syntax, method = \"dblcent\", match = FALSE, ...)"},{"path":"/reference/get_pi_syntax.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get lavaan syntax for product indicator approaches — get_pi_syntax","text":"model.syntax lavaan syntax method method use: \"rca\" = residual centering approach, \"uca\" = unconstrained approach, \"dblcent\" = double centering approach, \"pind\" = prod ind approach, constraints centering, \"custom\" = use parameters specified function call match product indicators created using match-strategy ... arguments passed functions (e.g., modsem_pi)","code":""},{"path":"/reference/get_pi_syntax.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get lavaan syntax for product indicator approaches — get_pi_syntax","text":"character vector","code":""},{"path":"/reference/get_pi_syntax.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Get lavaan syntax for product indicator approaches — get_pi_syntax","text":"","code":"library(modsem) library(lavaan) m1 <- ' # Outer Model X =~ x1 + x2 + x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' syntax <- get_pi_syntax(m1) data <- get_pi_data(m1, oneInt) est <- sem(syntax, data)"},{"path":"/reference/jordan.html","id":null,"dir":"Reference","previous_headings":"","what":"Jordan subset of PISA 2006 data — jordan","title":"Jordan subset of PISA 2006 data — jordan","text":"data stem large-scale assessment study PISA 2006 (Organisation Economic Co-Operation Development, 2009) competencies 15-year-old students reading, mathematics, science assessed using nationally representative samples 3-year cycles. eacademicample, data student background questionnaire Jordan sample PISA 2006 used. data students complete responses 15 items (N = 6,038) considered.","code":""},{"path":"/reference/jordan.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Jordan subset of PISA 2006 data — jordan","text":"data frame fifteen variables 6,038 observations: enjoy1 indicator enjoyment science, item ST16Q01: generally fun learning topics. enjoy2 indicator enjoyment science, item ST16Q02: like reading . enjoy3 indicator enjoyment science, item ST16Q03: happy problems. enjoy4 indicator enjoyment science, item ST16Q04: enjoy acquiring new knowledge . enjoy5 indicator enjoyment science, item ST16Q05: interested learning . academic1 indicator academic self-concept science, item ST37Q01: can easily understand new ideas . academic2 indicator academic self-concept science, item ST37Q02: Learning advanced topics easy . academic3 indicator academic self-concept science, item ST37Q03: can usually give good answers topics. academic4 indicator academic self-concept science, item ST37Q04: learn topics quickly. academic5 indicator academic self-concept science, item ST37Q05: topics easy . academic6 indicator academic self-concept science, item ST37Q06: taught , can understand concepts well. career1 indicator career aspirations science, item ST29Q01: like work career involving . career2 indicator career aspirations science, item ST29Q02: like study . career3 indicator career aspirations science, item ST29Q03: like spend life advanced . career4 indicator career aspirations science, item ST29Q04: like work projects adult.","code":""},{"path":"/reference/jordan.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Jordan subset of PISA 2006 data — jordan","text":"version dataset, well description gathered documentation 'nlsem' package (https://cran.r-project.org/package=nlsem), difference names variables changed Originally dataset gathered Organisation Economic Co-Operation Development (2009). Pisa 2006: Science competencies tomorrow's world (Tech. Rep.). Paris, France. Obtained : https://www.oecd.org/pisa/pisaproducts/database-pisa2006.htm","code":""},{"path":"/reference/jordan.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Jordan subset of PISA 2006 data — jordan","text":"","code":"if (FALSE) { # \\dontrun{ m1 <- ' ENJ =~ enjoy1 + enjoy2 + enjoy3 + enjoy4 + enjoy5 CAREER =~ career1 + career2 + career3 + career4 SC =~ academic1 + academic2 + academic3 + academic4 + academic5 + academic6 CAREER ~ ENJ + SC + ENJ:ENJ + SC:SC + ENJ:SC ' est <- modsem(m1, data = jordan) } # }"},{"path":"/reference/modsem-package.html","id":null,"dir":"Reference","previous_headings":"","what":"modsem: Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM) — modsem-package","title":"modsem: Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM) — modsem-package","text":"Estimation interaction (.e., moderation) effects latent variables structural equation models (SEM). supported methods : constrained approach (Algina & Moulder, 2001). unconstrained approach (Marsh et al., 2004). residual centering approach (Little et al., 2006). double centering approach (Lin et al., 2010). latent moderated structural equations (LMS) approach (Klein & Moosbrugger, 2000). quasi-maximum likelihood (QML) approach (Klein & Muthén, 2007) (temporarily unavailable) constrained- unconstrained, residual- double centering- approaches estimated via 'lavaan' (Rosseel, 2012), whilst LMS- QML- approaches estimated via modsem self. Alternatively model can estimated via 'Mplus' (Muthén & Muthén, 1998-2017). References: Algina, J., & Moulder, B. C. (2001). doi:10.1207/S15328007SEM0801_3 . \"note estimating Jöreskog-Yang model latent variable interaction using 'LISREL' 8.3.\" Klein, ., & Moosbrugger, H. (2000). doi:10.1007/BF02296338 . \"Maximum likelihood estimation latent interaction effects LMS method.\" Klein, . G., & Muthén, B. O. (2007). doi:10.1080/00273170701710205 . \"Quasi-maximum likelihood estimation structural equation models multiple interaction quadratic effects.\" Lin, G. C., Wen, Z., Marsh, H. W., & Lin, H. S. (2010). doi:10.1080/10705511.2010.488999 . \"Structural equation models latent interactions: Clarification orthogonalizing double-mean-centering strategies.\" Little, T. D., Bovaird, J. ., & Widaman, K. F. (2006). doi:10.1207/s15328007sem1304_1 . \"merits orthogonalizing powered product terms: Implications modeling interactions among latent variables.\" Marsh, H. W., Wen, Z., & Hau, K. T. (2004). doi:10.1037/1082-989X.9.3.275 . \"Structural equation models latent interactions: evaluation alternative estimation strategies indicator construction.\" Muthén, L.K. Muthén, B.O. (1998-2017). \"'Mplus' User’s Guide. Eighth Edition.\" https://www.statmodel.com/. Rosseel Y (2012). doi:10.18637/jss.v048.i02 . \"'lavaan': R Package Structural Equation Modeling.\"","code":""},{"path":[]},{"path":"/reference/modsem-package.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"modsem: Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM) — modsem-package","text":"Maintainer: Kjell Solem Slupphaug slupphaugkjell@gmail.com (ORCID)","code":""},{"path":"/reference/modsem.html","id":null,"dir":"Reference","previous_headings":"","what":"Estimate interaction effects in structural equation models (SEMs) — modsem","title":"Estimate interaction effects in structural equation models (SEMs) — modsem","text":"modsem() function estimating interaction effects latent variables structural equation models (SEMs). Methods estimating interaction effects SEMs can basically split two frameworks: 1. Product Indicator-based approaches (\"dblcent\", \"rca\", \"uca\", \"ca\", \"pind\") 2. Distributionally based approaches (\"lms\", \"qml\"). product indicator-based approaches, modsem() essentially fancy wrapper lavaan::sem() generates necessary syntax variables estimation models latent product indicators. distributionally based approaches implemented separately estimated using lavaan::sem(), rather using custom functions (largely written C++ performance reasons). greater control, advised use one sub-functions (modsem_pi, modsem_da, modsem_mplus) directly, passing additional arguments via modsem() can lead unexpected behavior.","code":""},{"path":"/reference/modsem.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Estimate interaction effects in structural equation models (SEMs) — modsem","text":"","code":"modsem(model.syntax = NULL, data = NULL, method = \"dblcent\", ...)"},{"path":"/reference/modsem.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Estimate interaction effects in structural equation models (SEMs) — modsem","text":"model.syntax lavaan syntax data dataframe method method use: \"rca\" = residual centering approach (passed lavaan), \"uca\" = unconstrained approach (passed lavaan), \"dblcent\" = double centering approach (passed lavaan), \"pind\" = prod ind approach, constraints centering (passed lavaan), \"lms\" = latent model structural equations (passed lavaan), \"qml\" = quasi maximum likelihood estimation latent model structural equations (passed lavaan), \"custom\" = use parameters specified function call (passed lavaan). ... arguments passed functions depending method (see modsem_pi, modsem_da, modsem_mplus)","code":""},{"path":"/reference/modsem.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Estimate interaction effects in structural equation models (SEMs) — modsem","text":"modsem object class modsem_pi, modsem_da, modsem_mplus","code":""},{"path":"/reference/modsem.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Estimate interaction effects in structural equation models (SEMs) — modsem","text":"","code":"library(modsem) # For more examples, check README and/or GitHub. # One interaction m1 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' # Double centering approach est1 <- modsem(m1, oneInt) summary(est1) #> modsem: #> Method = dblcent #> lavaan 0.6-19 ended normally after 159 iterations #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 60 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 122.924 #> Degrees of freedom 111 #> P-value (Chi-square) 0.207 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Latent Variables: #> Estimate Std.Err z-value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.804 0.013 63.612 0.000 #> x3 0.916 0.014 67.144 0.000 #> Y =~ #> y1 1.000 #> y2 0.798 0.007 107.428 0.000 #> y3 0.899 0.008 112.453 0.000 #> Z =~ #> z1 1.000 #> z2 0.812 0.013 64.763 0.000 #> z3 0.882 0.013 67.014 0.000 #> XZ =~ #> x1z1 1.000 #> x2z1 0.805 0.013 60.636 0.000 #> x3z1 0.877 0.014 62.680 0.000 #> x1z2 0.793 0.013 59.343 0.000 #> x2z2 0.646 0.015 43.672 0.000 #> x3z2 0.706 0.016 44.292 0.000 #> x1z3 0.887 0.014 63.700 0.000 #> x2z3 0.716 0.016 45.645 0.000 #> x3z3 0.781 0.017 45.339 0.000 #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> Y ~ #> X 0.675 0.027 25.379 0.000 #> Z 0.561 0.026 21.606 0.000 #> XZ 0.702 0.027 26.360 0.000 #> #> Covariances: #> Estimate Std.Err z-value P(>|z|) #> .x1z1 ~~ #> .x2z2 0.000 #> .x2z3 0.000 #> .x3z2 0.000 #> .x3z3 0.000 #> .x2z1 ~~ #> .x1z2 0.000 #> .x1z2 ~~ #> .x2z3 0.000 #> .x3z1 ~~ #> .x1z2 0.000 #> .x1z2 ~~ #> .x3z3 0.000 #> .x2z1 ~~ #> .x1z3 0.000 #> .x2z2 ~~ #> .x1z3 0.000 #> .x3z1 ~~ #> .x1z3 0.000 #> .x3z2 ~~ #> .x1z3 0.000 #> .x2z1 ~~ #> .x3z2 0.000 #> .x3z3 0.000 #> .x3z1 ~~ #> .x2z2 0.000 #> .x2z2 ~~ #> .x3z3 0.000 #> .x3z1 ~~ #> .x2z3 0.000 #> .x3z2 ~~ #> .x2z3 0.000 #> .x1z1 ~~ #> .x1z2 0.115 0.008 14.802 0.000 #> .x1z3 0.114 0.008 13.947 0.000 #> .x2z1 0.125 0.008 16.095 0.000 #> .x3z1 0.140 0.009 16.135 0.000 #> .x1z2 ~~ #> .x1z3 0.103 0.007 14.675 0.000 #> .x2z2 0.128 0.006 20.850 0.000 #> .x3z2 0.146 0.007 21.243 0.000 #> .x1z3 ~~ #> .x2z3 0.116 0.007 17.818 0.000 #> .x3z3 0.135 0.007 18.335 0.000 #> .x2z1 ~~ #> .x2z2 0.135 0.006 20.905 0.000 #> .x2z3 0.145 0.007 21.145 0.000 #> .x3z1 0.114 0.007 16.058 0.000 #> .x2z2 ~~ #> .x2z3 0.117 0.006 20.419 0.000 #> .x3z2 0.116 0.006 20.586 0.000 #> .x2z3 ~~ #> .x3z3 0.109 0.006 18.059 0.000 #> .x3z1 ~~ #> .x3z2 0.138 0.007 19.331 0.000 #> .x3z3 0.158 0.008 20.269 0.000 #> .x3z2 ~~ #> .x3z3 0.131 0.007 19.958 0.000 #> X ~~ #> Z 0.201 0.024 8.271 0.000 #> XZ 0.016 0.025 0.628 0.530 #> Z ~~ #> XZ 0.062 0.025 2.449 0.014 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .x1 0.160 0.009 17.871 0.000 #> .x2 0.162 0.007 22.969 0.000 #> .x3 0.163 0.008 20.161 0.000 #> .y1 0.159 0.009 17.896 0.000 #> .y2 0.154 0.007 22.640 0.000 #> .y3 0.164 0.008 20.698 0.000 #> .z1 0.168 0.009 18.143 0.000 #> .z2 0.158 0.007 22.264 0.000 #> .z3 0.158 0.008 20.389 0.000 #> .x1z1 0.311 0.014 22.227 0.000 #> .x2z1 0.292 0.011 27.287 0.000 #> .x3z1 0.327 0.012 26.275 0.000 #> .x1z2 0.290 0.011 26.910 0.000 #> .x2z2 0.239 0.008 29.770 0.000 #> .x3z2 0.270 0.009 29.117 0.000 #> .x1z3 0.272 0.012 23.586 0.000 #> .x2z3 0.245 0.009 27.979 0.000 #> .x3z3 0.297 0.011 28.154 0.000 #> X 0.981 0.036 26.895 0.000 #> .Y 0.990 0.038 25.926 0.000 #> Z 1.016 0.038 26.856 0.000 #> XZ 1.045 0.044 24.004 0.000 #> if (FALSE) { # \\dontrun{ # The Constrained Approach est1_ca <- modsem(m1, oneInt, method = \"ca\") summary(est1_ca) # LMS approach est1_lms <- modsem(m1, oneInt, method = \"lms\") summary(est1_lms) # QML approach est1_qml <- modsem(m1, oneInt, method = \"qml\") summary(est1_qml) } # } # Theory Of Planned Behavior tpb <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ INT:PBC ' # Double centering approach est_tpb <- modsem(tpb, data = TPB) summary(est_tpb) #> modsem: #> Method = dblcent #> lavaan 0.6-19 ended normally after 171 iterations #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 78 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 207.615 #> Degrees of freedom 222 #> P-value (Chi-square) 0.747 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Latent Variables: #> Estimate Std.Err z-value P(>|z|) #> ATT =~ #> att1 1.000 #> att2 0.878 0.012 71.509 0.000 #> att3 0.789 0.012 66.368 0.000 #> att4 0.695 0.011 61.017 0.000 #> att5 0.887 0.013 70.884 0.000 #> SN =~ #> sn1 1.000 #> sn2 0.889 0.017 52.553 0.000 #> PBC =~ #> pbc1 1.000 #> pbc2 0.912 0.013 69.500 0.000 #> pbc3 0.801 0.012 65.830 0.000 #> INT =~ #> int1 1.000 #> int2 0.914 0.016 58.982 0.000 #> int3 0.808 0.015 55.547 0.000 #> BEH =~ #> b1 1.000 #> b2 0.960 0.030 31.561 0.000 #> INTPBC =~ #> int1pbc1 1.000 #> int2pbc1 0.931 0.015 63.809 0.000 #> int3pbc1 0.774 0.013 60.107 0.000 #> int1pbc2 0.893 0.013 68.173 0.000 #> int2pbc2 0.826 0.017 48.845 0.000 #> int3pbc2 0.690 0.015 45.300 0.000 #> int1pbc3 0.799 0.012 67.008 0.000 #> int2pbc3 0.738 0.015 47.809 0.000 #> int3pbc3 0.622 0.014 45.465 0.000 #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> INT ~ #> ATT 0.213 0.026 8.170 0.000 #> SN 0.177 0.028 6.416 0.000 #> PBC 0.217 0.030 7.340 0.000 #> BEH ~ #> INT 0.191 0.024 7.817 0.000 #> PBC 0.230 0.022 10.507 0.000 #> INTPBC 0.204 0.018 11.425 0.000 #> #> Covariances: #> Estimate Std.Err z-value P(>|z|) #> .int1pbc1 ~~ #> .int2pbc2 0.000 #> .int2pbc3 0.000 #> .int3pbc2 0.000 #> .int3pbc3 0.000 #> .int2pbc1 ~~ #> .int1pbc2 0.000 #> .int1pbc2 ~~ #> .int2pbc3 0.000 #> .int3pbc1 ~~ #> .int1pbc2 0.000 #> .int1pbc2 ~~ #> .int3pbc3 0.000 #> .int2pbc1 ~~ #> .int1pbc3 0.000 #> .int2pbc2 ~~ #> .int1pbc3 0.000 #> .int3pbc1 ~~ #> .int1pbc3 0.000 #> .int3pbc2 ~~ #> .int1pbc3 0.000 #> .int2pbc1 ~~ #> .int3pbc2 0.000 #> .int3pbc3 0.000 #> .int3pbc1 ~~ #> .int2pbc2 0.000 #> .int2pbc2 ~~ #> .int3pbc3 0.000 #> .int3pbc1 ~~ #> .int2pbc3 0.000 #> .int3pbc2 ~~ #> .int2pbc3 0.000 #> .int1pbc1 ~~ #> .int1pbc2 0.126 0.009 14.768 0.000 #> .int1pbc3 0.102 0.007 13.794 0.000 #> .int2pbc1 0.104 0.007 14.608 0.000 #> .int3pbc1 0.091 0.006 14.109 0.000 #> .int1pbc2 ~~ #> .int1pbc3 0.095 0.007 13.852 0.000 #> .int2pbc2 0.128 0.007 19.320 0.000 #> .int3pbc2 0.119 0.006 19.402 0.000 #> .int1pbc3 ~~ #> .int2pbc3 0.110 0.006 19.911 0.000 #> .int3pbc3 0.097 0.005 19.415 0.000 #> .int2pbc1 ~~ #> .int2pbc2 0.152 0.008 18.665 0.000 #> .int2pbc3 0.138 0.007 18.779 0.000 #> .int3pbc1 0.082 0.006 13.951 0.000 #> .int2pbc2 ~~ #> .int2pbc3 0.121 0.007 18.361 0.000 #> .int3pbc2 0.104 0.005 19.047 0.000 #> .int2pbc3 ~~ #> .int3pbc3 0.087 0.005 19.180 0.000 #> .int3pbc1 ~~ #> .int3pbc2 0.139 0.007 21.210 0.000 #> .int3pbc3 0.123 0.006 21.059 0.000 #> .int3pbc2 ~~ #> .int3pbc3 0.114 0.005 21.021 0.000 #> ATT ~~ #> SN 0.629 0.029 21.977 0.000 #> PBC 0.678 0.029 23.721 0.000 #> INTPBC 0.086 0.024 3.519 0.000 #> SN ~~ #> PBC 0.678 0.029 23.338 0.000 #> INTPBC 0.055 0.025 2.230 0.026 #> PBC ~~ #> INTPBC 0.087 0.024 3.609 0.000 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .att1 0.167 0.007 23.528 0.000 #> .att2 0.150 0.006 24.693 0.000 #> .att3 0.160 0.006 26.378 0.000 #> .att4 0.163 0.006 27.649 0.000 #> .att5 0.159 0.006 24.930 0.000 #> .sn1 0.178 0.015 12.110 0.000 #> .sn2 0.156 0.012 13.221 0.000 #> .pbc1 0.145 0.008 18.440 0.000 #> .pbc2 0.160 0.007 21.547 0.000 #> .pbc3 0.154 0.007 23.716 0.000 #> .int1 0.158 0.009 18.152 0.000 #> .int2 0.160 0.008 20.345 0.000 #> .int3 0.167 0.007 23.414 0.000 #> .b1 0.186 0.018 10.058 0.000 #> .b2 0.135 0.017 8.080 0.000 #> .int1pbc1 0.266 0.013 20.971 0.000 #> .int2pbc1 0.292 0.012 24.421 0.000 #> .int3pbc1 0.251 0.010 26.305 0.000 #> .int1pbc2 0.290 0.012 24.929 0.000 #> .int2pbc2 0.269 0.010 26.701 0.000 #> .int3pbc2 0.253 0.009 29.445 0.000 #> .int1pbc3 0.223 0.009 24.431 0.000 #> .int2pbc3 0.234 0.008 27.633 0.000 #> .int3pbc3 0.203 0.007 29.288 0.000 #> ATT 0.998 0.037 27.138 0.000 #> SN 0.987 0.039 25.394 0.000 #> PBC 0.962 0.035 27.260 0.000 #> .INT 0.490 0.020 24.638 0.000 #> .BEH 0.455 0.023 20.068 0.000 #> INTPBC 1.020 0.041 24.612 0.000 #> if (FALSE) { # \\dontrun{ # The Constrained Approach est_tpb_ca <- modsem(tpb, data = TPB, method = \"ca\") summary(est_tpb_ca) # LMS approach est_tpb_lms <- modsem(tpb, data = TPB, method = \"lms\") summary(est_tpb_lms) # QML approach est_tpb_qml <- modsem(tpb, data = TPB, method = \"qml\") summary(est_tpb_qml) } # }"},{"path":"/reference/modsem_da.html","id":null,"dir":"Reference","previous_headings":"","what":"Interaction between latent variables using lms and qml approaches — modsem_da","title":"Interaction between latent variables using lms and qml approaches — modsem_da","text":"modsem_da() function estimating interaction effects latent variables structural equation models (SEMs) using distributional analytic (DA) approaches. Methods estimating interaction effects SEMs can basically split two frameworks: 1. Product Indicator-based approaches (\"dblcent\", \"rca\", \"uca\", \"ca\", \"pind\") 2. Distributionally based approaches (\"lms\", \"qml\"). modsem_da() handles latter can estimate models using QML LMS, necessary syntax, variables estimation models latent product indicators. NOTE: Run default_settings_da see default arguments.","code":""},{"path":"/reference/modsem_da.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Interaction between latent variables using lms and qml approaches — modsem_da","text":"","code":"modsem_da( model.syntax = NULL, data = NULL, method = \"lms\", verbose = NULL, optimize = NULL, nodes = NULL, convergence = NULL, optimizer = NULL, center.data = NULL, standardize.data = NULL, standardize.out = NULL, standardize = NULL, mean.observed = NULL, cov.syntax = NULL, double = NULL, calc.se = NULL, FIM = NULL, EFIM.S = NULL, OFIM.hessian = NULL, EFIM.parametric = NULL, robust.se = NULL, max.iter = NULL, max.step = NULL, fix.estep = NULL, start = NULL, epsilon = NULL, quad.range = NULL, n.threads = NULL, ... )"},{"path":"/reference/modsem_da.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Interaction between latent variables using lms and qml approaches — modsem_da","text":"model.syntax lavaan syntax data dataframe method method use: \"lms\" = latent model structural equations (passed lavaan). \"qml\" = quasi maximum likelihood estimation latent model structural equations (passed lavaan). verbose estimation progress shown optimize starting parameters optimized nodes number quadrature nodes (points integration) used lms, increased number gives better estimates slower computation. many needed depends complexity model. simple models, somewhere 16-24 nodes enough; complex models, higher numbers may needed. models interaction effect endogenous exogenous variable, number nodes least 32, practically (e.g., ordinal/skewed data), 32 recommended. cases data non-normal, might better use qml approach instead. large numbers nodes, might want change 'quad.range' argument. convergence convergence criterion. Lower values give better estimates slower computation. optimizer optimizer use, can either \"nlminb\" \"L-BFGS-B\". LMS, \"nlminb\" recommended. QML, \"L-BFGS-B\" may faster large number iterations, slower iterations. center.data data centered fitting model standardize.data data scaled fitting model, overridden standardize standardize set TRUE. NOTE: recommended estimate model normally standardize output using standardized_estimates. standardize.output standardized (note alter relationships parameter constraints since parameters scaled unevenly, even label). alter estimation model, output. NOTE: recommended estimate model normally standardize output using standardized_estimates. standardize standardize data fitting model, remove mean structure observed variables, standardize output. Note standardize.data, mean.observed, standardize.overridden standardize standardize set TRUE. NOTE: recommended estimate model normally standardize output using standardized_estimates. mean.observed mean structure observed variables estimated? overridden standardize standardize set TRUE. NOTE: recommended unless know . cov.syntax model syntax implied covariance matrix (see vignette(\"interaction_two_etas\", \"modsem\")) double try double number dimensions integration used LMS, extremely slow similar mplus. calc.se standard errors computed? NOTE: FALSE, information matrix computed either. FIM Fisher information matrix calculated using observed expected values? Must either \"observed\" \"expected\". EFIM.S expected Fisher information matrix computed, EFIM.S selects sample size generated data. OFIM.hessian observed Fisher information computed using Hessian? FALSE, computed using gradient. EFIM.parametric data calculating expected Fisher information matrix simulated parametrically (simulated based assumptions implied parameters model), non-parametrically (stochastically sampled)? believe normality assumptions violated, EFIM.parametric = FALSE might better option. robust.se robust standard errors computed? Meant used QML, can unreliable LMS approach. max.iter maximum number iterations. max.step maximum steps M-step EM algorithm (LMS). fix.estep TRUE, E-step fixed, prior probabilities set best prior probabilities, log-likelihood decreases 30 iterations. start starting parameters. epsilon finite difference numerical derivatives. quad.range range z-scores perform numerical integration LMS using Gaussian-Hermite Quadratures. default Inf, f(t) integrated -Inf Inf, likely inefficient pointless large number nodes. Nodes outside +/- quad.range ignored. n.threads number cores use parallel processing. NULL, use <= 2 threads. integer specified, use number threads (e.g., n.threads = 4 use 4 threads). \"default\", use default number threads (2). \"max\", use available threads, \"min\" use 1 thread. ... additional arguments passed estimation function.","code":""},{"path":"/reference/modsem_da.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Interaction between latent variables using lms and qml approaches — modsem_da","text":"modsem_da object","code":""},{"path":"/reference/modsem_da.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Interaction between latent variables using lms and qml approaches — modsem_da","text":"","code":"library(modsem) # For more examples, check README and/or GitHub. # One interaction m1 <- \" # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z \" if (FALSE) { # \\dontrun{ # QML Approach est1 <- modsem_da(m1, oneInt, method = \"qml\") summary(est1) # Theory Of Planned Behavior tpb <- \" # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) # Covariances ATT ~~ SN + PBC PBC ~~ SN # Causal Relationships INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ INT:PBC \" # LMS Approach estTpb <- modsem_da(tpb, data = TPB, method = lms) summary(estTpb) } # }"},{"path":"/reference/modsem_inspect.html","id":null,"dir":"Reference","previous_headings":"","what":"Inspect model information — modsem_inspect","title":"Inspect model information — modsem_inspect","text":"function used inspect fittet object. similar `lavInspect()` argument '' decides inspect","code":""},{"path":"/reference/modsem_inspect.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Inspect model information — modsem_inspect","text":"","code":"modsem_inspect(object, what = NULL, ...)"},{"path":"/reference/modsem_inspect.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Inspect model information — modsem_inspect","text":"object fittet model inspect inspect ... Additional arguments passed functions","code":""},{"path":"/reference/modsem_inspect.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Inspect model information — modsem_inspect","text":"`modsem_da`, `modsem_lavaan` `modsem_lavaan`, just wrapper `lavInspect()` `modsem_da` “ can either \"\", \"matrices\", \"optim\", just name extract.","code":""},{"path":"/reference/modsem_mplus.html","id":null,"dir":"Reference","previous_headings":"","what":"Estimation latent interactions through mplus — modsem_mplus","title":"Estimation latent interactions through mplus — modsem_mplus","text":"Estimation latent interactions mplus","code":""},{"path":"/reference/modsem_mplus.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Estimation latent interactions through mplus — modsem_mplus","text":"","code":"modsem_mplus( model.syntax, data, estimator = \"ml\", type = \"random\", algorithm = \"integration\", process = \"8\", ... )"},{"path":"/reference/modsem_mplus.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Estimation latent interactions through mplus — modsem_mplus","text":"model.syntax lavaan/modsem syntax data dataset estimator estimator argument passed mplus type type argument passed mplus algorithm algorithm argument passed mplus process process argument passed mplus ... arguments passed functions","code":""},{"path":"/reference/modsem_mplus.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Estimation latent interactions through mplus — modsem_mplus","text":"modsem_mplus object","code":""},{"path":"/reference/modsem_mplus.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Estimation latent interactions through mplus — modsem_mplus","text":"","code":"# Theory Of Planned Behavior tpb <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) # Covariances ATT ~~ SN + PBC PBC ~~ SN # Causal Relationsships INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ INT:PBC ' if (FALSE) { # \\dontrun{ estTpbMplus <- modsem_mplus(tpb, data = TPB) summary(estTpbLMS) } # }"},{"path":"/reference/modsem_pi.html","id":null,"dir":"Reference","previous_headings":"","what":"Interaction between latent variables using product indicators — modsem_pi","title":"Interaction between latent variables using product indicators — modsem_pi","text":"modsem_pi() function estimating interaction effects latent variables, structural equation models (SEMs), using product indicators. Methods estimating interaction effects SEMs can basically split two frameworks: 1. Product Indicator based approaches (\"dblcent\", \"rca\", \"uca\", \"ca\", \"pind\"), 2. Distributionally based approaches (\"lms\", \"qml\"). modsem_pi() essentially fancy wrapper lavaan::sem() generates necessary syntax variables estimation models latent product indicators. Use default_settings_pi() get default settings different methods.","code":""},{"path":"/reference/modsem_pi.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Interaction between latent variables using product indicators — modsem_pi","text":"","code":"modsem_pi( model.syntax = NULL, data = NULL, method = \"dblcent\", match = NULL, standardize.data = FALSE, center.data = FALSE, first.loading.fixed = TRUE, center.before = NULL, center.after = NULL, residuals.prods = NULL, residual.cov.syntax = NULL, constrained.prod.mean = NULL, constrained.loadings = NULL, constrained.var = NULL, constrained.res.cov.method = NULL, auto.scale = \"none\", auto.center = \"none\", estimator = \"ML\", group = NULL, run = TRUE, suppress.warnings.lavaan = FALSE, ... )"},{"path":"/reference/modsem_pi.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Interaction between latent variables using product indicators — modsem_pi","text":"model.syntax lavaan syntax data dataframe method method use: \"rca\" = residual centering approach (passed lavaan), \"uca\" = unconstrained approach (passed lavaan), \"dblcent\" = double centering approach (passed lavaan), \"pind\" = prod ind approach, constraints centering (passed lavaan), \"custom\" = use parameters specified function call (passed lavaan) match product indicators created using match-strategy standardize.data data scaled fitting model center.data data centered fitting model first.loading.fixed first factor loading latent product fixed one? center.indicators products centered computing products (overwritten method, method != NULL) center.indicator products centered computed? residuals.prods indicator products centered using residuals (overwritten method, method != NULL) residual.cov.syntax syntax residual covariances produced (overwritten method, method != NULL) constrained.prod.mean syntax product mean produced (overwritten method, method != NULL) constrained.loadings syntax constrained loadings produced (overwritten method, method != NULL) constrained.var syntax constrained variances produced (overwritten method, method != NULL) constrained.res.cov.method method constraining residual covariances auto.scale methods scaled automatically (usually useful) auto.center methods centered automatically (usually useful) estimator estimator use lavaan group group variable multigroup analysis run model run via lavaan, FALSE modified syntax data returned suppress.warnings.lavaan warnings lavaan suppressed? ... arguments passed functions, e.g., lavaan","code":""},{"path":"/reference/modsem_pi.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Interaction between latent variables using product indicators — modsem_pi","text":"modsem object","code":""},{"path":"/reference/modsem_pi.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Interaction between latent variables using product indicators — modsem_pi","text":"","code":"library(modsem) # For more examples, check README and/or GitHub. # One interaction m1 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' # Double centering approach est1 <- modsem_pi(m1, oneInt) summary(est1) #> modsem: #> Method = dblcent #> lavaan 0.6-19 ended normally after 159 iterations #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 60 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 122.924 #> Degrees of freedom 111 #> P-value (Chi-square) 0.207 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Latent Variables: #> Estimate Std.Err z-value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.804 0.013 63.612 0.000 #> x3 0.916 0.014 67.144 0.000 #> Y =~ #> y1 1.000 #> y2 0.798 0.007 107.428 0.000 #> y3 0.899 0.008 112.453 0.000 #> Z =~ #> z1 1.000 #> z2 0.812 0.013 64.763 0.000 #> z3 0.882 0.013 67.014 0.000 #> XZ =~ #> x1z1 1.000 #> x2z1 0.805 0.013 60.636 0.000 #> x3z1 0.877 0.014 62.680 0.000 #> x1z2 0.793 0.013 59.343 0.000 #> x2z2 0.646 0.015 43.672 0.000 #> x3z2 0.706 0.016 44.292 0.000 #> x1z3 0.887 0.014 63.700 0.000 #> x2z3 0.716 0.016 45.645 0.000 #> x3z3 0.781 0.017 45.339 0.000 #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> Y ~ #> X 0.675 0.027 25.379 0.000 #> Z 0.561 0.026 21.606 0.000 #> XZ 0.702 0.027 26.360 0.000 #> #> Covariances: #> Estimate Std.Err z-value P(>|z|) #> .x1z1 ~~ #> .x2z2 0.000 #> .x2z3 0.000 #> .x3z2 0.000 #> .x3z3 0.000 #> .x2z1 ~~ #> .x1z2 0.000 #> .x1z2 ~~ #> .x2z3 0.000 #> .x3z1 ~~ #> .x1z2 0.000 #> .x1z2 ~~ #> .x3z3 0.000 #> .x2z1 ~~ #> .x1z3 0.000 #> .x2z2 ~~ #> .x1z3 0.000 #> .x3z1 ~~ #> .x1z3 0.000 #> .x3z2 ~~ #> .x1z3 0.000 #> .x2z1 ~~ #> .x3z2 0.000 #> .x3z3 0.000 #> .x3z1 ~~ #> .x2z2 0.000 #> .x2z2 ~~ #> .x3z3 0.000 #> .x3z1 ~~ #> .x2z3 0.000 #> .x3z2 ~~ #> .x2z3 0.000 #> .x1z1 ~~ #> .x1z2 0.115 0.008 14.802 0.000 #> .x1z3 0.114 0.008 13.947 0.000 #> .x2z1 0.125 0.008 16.095 0.000 #> .x3z1 0.140 0.009 16.135 0.000 #> .x1z2 ~~ #> .x1z3 0.103 0.007 14.675 0.000 #> .x2z2 0.128 0.006 20.850 0.000 #> .x3z2 0.146 0.007 21.243 0.000 #> .x1z3 ~~ #> .x2z3 0.116 0.007 17.818 0.000 #> .x3z3 0.135 0.007 18.335 0.000 #> .x2z1 ~~ #> .x2z2 0.135 0.006 20.905 0.000 #> .x2z3 0.145 0.007 21.145 0.000 #> .x3z1 0.114 0.007 16.058 0.000 #> .x2z2 ~~ #> .x2z3 0.117 0.006 20.419 0.000 #> .x3z2 0.116 0.006 20.586 0.000 #> .x2z3 ~~ #> .x3z3 0.109 0.006 18.059 0.000 #> .x3z1 ~~ #> .x3z2 0.138 0.007 19.331 0.000 #> .x3z3 0.158 0.008 20.269 0.000 #> .x3z2 ~~ #> .x3z3 0.131 0.007 19.958 0.000 #> X ~~ #> Z 0.201 0.024 8.271 0.000 #> XZ 0.016 0.025 0.628 0.530 #> Z ~~ #> XZ 0.062 0.025 2.449 0.014 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .x1 0.160 0.009 17.871 0.000 #> .x2 0.162 0.007 22.969 0.000 #> .x3 0.163 0.008 20.161 0.000 #> .y1 0.159 0.009 17.896 0.000 #> .y2 0.154 0.007 22.640 0.000 #> .y3 0.164 0.008 20.698 0.000 #> .z1 0.168 0.009 18.143 0.000 #> .z2 0.158 0.007 22.264 0.000 #> .z3 0.158 0.008 20.389 0.000 #> .x1z1 0.311 0.014 22.227 0.000 #> .x2z1 0.292 0.011 27.287 0.000 #> .x3z1 0.327 0.012 26.275 0.000 #> .x1z2 0.290 0.011 26.910 0.000 #> .x2z2 0.239 0.008 29.770 0.000 #> .x3z2 0.270 0.009 29.117 0.000 #> .x1z3 0.272 0.012 23.586 0.000 #> .x2z3 0.245 0.009 27.979 0.000 #> .x3z3 0.297 0.011 28.154 0.000 #> X 0.981 0.036 26.895 0.000 #> .Y 0.990 0.038 25.926 0.000 #> Z 1.016 0.038 26.856 0.000 #> XZ 1.045 0.044 24.004 0.000 #> if (FALSE) { # \\dontrun{ # The Constrained Approach est1Constrained <- modsem_pi(m1, oneInt, method = \"ca\") summary(est1Constrained) } # } # Theory Of Planned Behavior tpb <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) # Covariances ATT ~~ SN + PBC PBC ~~ SN # Causal Relationships INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ INT:PBC ' # Double centering approach estTpb <- modsem_pi(tpb, data = TPB) summary(estTpb) #> modsem: #> Method = dblcent #> lavaan 0.6-19 ended normally after 169 iterations #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 78 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 207.615 #> Degrees of freedom 222 #> P-value (Chi-square) 0.747 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Latent Variables: #> Estimate Std.Err z-value P(>|z|) #> ATT =~ #> att1 1.000 #> att2 0.878 0.012 71.509 0.000 #> att3 0.789 0.012 66.368 0.000 #> att4 0.695 0.011 61.017 0.000 #> att5 0.887 0.013 70.884 0.000 #> SN =~ #> sn1 1.000 #> sn2 0.889 0.017 52.553 0.000 #> PBC =~ #> pbc1 1.000 #> pbc2 0.912 0.013 69.500 0.000 #> pbc3 0.801 0.012 65.830 0.000 #> INT =~ #> int1 1.000 #> int2 0.914 0.016 58.982 0.000 #> int3 0.808 0.015 55.547 0.000 #> BEH =~ #> b1 1.000 #> b2 0.960 0.030 31.561 0.000 #> INTPBC =~ #> int1pbc1 1.000 #> int2pbc1 0.931 0.015 63.809 0.000 #> int3pbc1 0.774 0.013 60.107 0.000 #> int1pbc2 0.893 0.013 68.172 0.000 #> int2pbc2 0.826 0.017 48.845 0.000 #> int3pbc2 0.690 0.015 45.300 0.000 #> int1pbc3 0.799 0.012 67.008 0.000 #> int2pbc3 0.738 0.015 47.809 0.000 #> int3pbc3 0.622 0.014 45.465 0.000 #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> INT ~ #> ATT 0.213 0.026 8.170 0.000 #> SN 0.177 0.028 6.416 0.000 #> PBC 0.217 0.030 7.340 0.000 #> BEH ~ #> INT 0.191 0.024 7.817 0.000 #> PBC 0.230 0.022 10.507 0.000 #> INTPBC 0.204 0.018 11.425 0.000 #> #> Covariances: #> Estimate Std.Err z-value P(>|z|) #> ATT ~~ #> SN 0.629 0.029 21.977 0.000 #> PBC 0.678 0.029 23.721 0.000 #> SN ~~ #> PBC 0.678 0.029 23.338 0.000 #> .int1pbc1 ~~ #> .int2pbc2 0.000 #> .int2pbc3 0.000 #> .int3pbc2 0.000 #> .int3pbc3 0.000 #> .int2pbc1 ~~ #> .int1pbc2 0.000 #> .int1pbc2 ~~ #> .int2pbc3 0.000 #> .int3pbc1 ~~ #> .int1pbc2 0.000 #> .int1pbc2 ~~ #> .int3pbc3 0.000 #> .int2pbc1 ~~ #> .int1pbc3 0.000 #> .int2pbc2 ~~ #> .int1pbc3 0.000 #> .int3pbc1 ~~ #> .int1pbc3 0.000 #> .int3pbc2 ~~ #> .int1pbc3 0.000 #> .int2pbc1 ~~ #> .int3pbc2 0.000 #> .int3pbc3 0.000 #> .int3pbc1 ~~ #> .int2pbc2 0.000 #> .int2pbc2 ~~ #> .int3pbc3 0.000 #> .int3pbc1 ~~ #> .int2pbc3 0.000 #> .int3pbc2 ~~ #> .int2pbc3 0.000 #> .int1pbc1 ~~ #> .int1pbc2 0.126 0.009 14.768 0.000 #> .int1pbc3 0.102 0.007 13.794 0.000 #> .int2pbc1 0.104 0.007 14.608 0.000 #> .int3pbc1 0.091 0.006 14.109 0.000 #> .int1pbc2 ~~ #> .int1pbc3 0.095 0.007 13.852 0.000 #> .int2pbc2 0.128 0.007 19.320 0.000 #> .int3pbc2 0.119 0.006 19.402 0.000 #> .int1pbc3 ~~ #> .int2pbc3 0.110 0.006 19.911 0.000 #> .int3pbc3 0.097 0.005 19.415 0.000 #> .int2pbc1 ~~ #> .int2pbc2 0.152 0.008 18.665 0.000 #> .int2pbc3 0.138 0.007 18.779 0.000 #> .int3pbc1 0.082 0.006 13.951 0.000 #> .int2pbc2 ~~ #> .int2pbc3 0.121 0.007 18.361 0.000 #> .int3pbc2 0.104 0.005 19.047 0.000 #> .int2pbc3 ~~ #> .int3pbc3 0.087 0.005 19.180 0.000 #> .int3pbc1 ~~ #> .int3pbc2 0.139 0.007 21.210 0.000 #> .int3pbc3 0.123 0.006 21.059 0.000 #> .int3pbc2 ~~ #> .int3pbc3 0.114 0.005 21.021 0.000 #> ATT ~~ #> INTPBC 0.086 0.024 3.519 0.000 #> SN ~~ #> INTPBC 0.055 0.025 2.230 0.026 #> PBC ~~ #> INTPBC 0.087 0.024 3.609 0.000 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .att1 0.167 0.007 23.528 0.000 #> .att2 0.150 0.006 24.693 0.000 #> .att3 0.160 0.006 26.378 0.000 #> .att4 0.163 0.006 27.649 0.000 #> .att5 0.159 0.006 24.930 0.000 #> .sn1 0.178 0.015 12.110 0.000 #> .sn2 0.156 0.012 13.221 0.000 #> .pbc1 0.145 0.008 18.440 0.000 #> .pbc2 0.160 0.007 21.547 0.000 #> .pbc3 0.154 0.007 23.716 0.000 #> .int1 0.158 0.009 18.152 0.000 #> .int2 0.160 0.008 20.345 0.000 #> .int3 0.167 0.007 23.414 0.000 #> .b1 0.186 0.018 10.058 0.000 #> .b2 0.135 0.017 8.080 0.000 #> .int1pbc1 0.266 0.013 20.971 0.000 #> .int2pbc1 0.292 0.012 24.421 0.000 #> .int3pbc1 0.251 0.010 26.305 0.000 #> .int1pbc2 0.290 0.012 24.929 0.000 #> .int2pbc2 0.269 0.010 26.701 0.000 #> .int3pbc2 0.253 0.009 29.445 0.000 #> .int1pbc3 0.223 0.009 24.431 0.000 #> .int2pbc3 0.234 0.008 27.633 0.000 #> .int3pbc3 0.203 0.007 29.288 0.000 #> ATT 0.998 0.037 27.138 0.000 #> SN 0.987 0.039 25.394 0.000 #> PBC 0.962 0.035 27.260 0.000 #> .INT 0.490 0.020 24.638 0.000 #> .BEH 0.455 0.023 20.068 0.000 #> INTPBC 1.020 0.041 24.612 0.000 #> if (FALSE) { # \\dontrun{ # The Constrained Approach estTpbConstrained <- modsem_pi(tpb, data = TPB, method = \"ca\") summary(estTpbConstrained) } # }"},{"path":"/reference/modsemify.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate parameter table for lavaan syntax — modsemify","title":"Generate parameter table for lavaan syntax — modsemify","text":"Generate parameter table lavaan syntax","code":""},{"path":"/reference/modsemify.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate parameter table for lavaan syntax — modsemify","text":"","code":"modsemify(syntax)"},{"path":"/reference/modsemify.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate parameter table for lavaan syntax — modsemify","text":"syntax model syntax","code":""},{"path":"/reference/modsemify.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate parameter table for lavaan syntax — modsemify","text":"data.frame columns lhs, op, rhs, mod","code":""},{"path":"/reference/modsemify.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate parameter table for lavaan syntax — modsemify","text":"","code":"library(modsem) m1 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' modsemify(m1) #> lhs op rhs mod #> 1 X =~ x1 #> 2 X =~ x2 #> 3 X =~ x3 #> 4 Y =~ y1 #> 5 Y =~ y2 #> 6 Y =~ y3 #> 7 Z =~ z1 #> 8 Z =~ z2 #> 9 Z =~ z3 #> 10 Y ~ X #> 11 Y ~ Z #> 12 Y ~ X:Z"},{"path":"/reference/multiplyIndicatorsCpp.html","id":null,"dir":"Reference","previous_headings":"","what":"Multiply indicators — multiplyIndicatorsCpp","title":"Multiply indicators — multiplyIndicatorsCpp","text":"Multiply indicators","code":""},{"path":"/reference/multiplyIndicatorsCpp.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Multiply indicators — multiplyIndicatorsCpp","text":"","code":"multiplyIndicatorsCpp(df)"},{"path":"/reference/multiplyIndicatorsCpp.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Multiply indicators — multiplyIndicatorsCpp","text":"df data DataFrame","code":""},{"path":"/reference/multiplyIndicatorsCpp.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Multiply indicators — multiplyIndicatorsCpp","text":"NumericVector","code":""},{"path":"/reference/oneInt.html","id":null,"dir":"Reference","previous_headings":"","what":"oneInt — oneInt","title":"oneInt — oneInt","text":"simulated dataset one interaction effect","code":""},{"path":"/reference/parameter_estimates.html","id":null,"dir":"Reference","previous_headings":"","what":"Extract parameterEstimates from an estimated model — parameter_estimates","title":"Extract parameterEstimates from an estimated model — parameter_estimates","text":"Extract parameterEstimates estimated model","code":""},{"path":"/reference/parameter_estimates.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Extract parameterEstimates from an estimated model — parameter_estimates","text":"","code":"parameter_estimates(object, ...)"},{"path":"/reference/parameter_estimates.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Extract parameterEstimates from an estimated model — parameter_estimates","text":"object object class modsem_pi, modsem_da, modsem_mplus ... Additional arguments passed functions","code":""},{"path":"/reference/plot_interaction.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot Interaction Effects — plot_interaction","title":"Plot Interaction Effects — plot_interaction","text":"Plot Interaction Effects","code":""},{"path":"/reference/plot_interaction.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot Interaction Effects — plot_interaction","text":"","code":"plot_interaction( x, z, y, xz = NULL, vals_x = seq(-3, 3, 0.001), vals_z, model, alpha_se = 0.15, ... )"},{"path":"/reference/plot_interaction.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot Interaction Effects — plot_interaction","text":"x name variable x-axis z name moderator variable y name outcome variable xz name interaction term. interaction term specified, created using x z. vals_x values x variable plot, values smoother std.error-area vals_z values moderator variable plot. separate regression line (y ~ x | z) plotted value moderator variable model object class modsem_pi, modsem_da, modsem_mplus alpha_se alpha level std.error area ... Additional arguments passed functions","code":""},{"path":"/reference/plot_interaction.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Plot Interaction Effects — plot_interaction","text":"ggplot object","code":""},{"path":"/reference/plot_interaction.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot Interaction Effects — plot_interaction","text":"","code":"library(modsem) if (FALSE) { # \\dontrun{ m1 <- \" # Outer Model X =~ x1 X =~ x2 + x3 Z =~ z1 + z2 + z3 Y =~ y1 + y2 + y3 # Inner model Y ~ X + Z + X:Z \" est1 <- modsem(m1, data = oneInt) plot_interaction(\"X\", \"Z\", \"Y\", \"X:Z\", -3:3, c(-0.2, 0), est1) tpb <- \" # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) # Causal Relationsships INT ~ ATT + SN + PBC BEH ~ INT + PBC # BEH ~ ATT:PBC BEH ~ PBC:INT # BEH ~ PBC:PBC \" est2 <- modsem(tpb, TPB, method = \"lms\") plot_interaction(x = \"INT\", z = \"PBC\", y = \"BEH\", xz = \"PBC:INT\", vals_z = c(-0.5, 0.5), model = est2) } # }"},{"path":"/reference/standardized_estimates.html","id":null,"dir":"Reference","previous_headings":"","what":"Get standardized estimates — standardized_estimates","title":"Get standardized estimates — standardized_estimates","text":"Get standardized estimates","code":""},{"path":"/reference/standardized_estimates.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get standardized estimates — standardized_estimates","text":"","code":"standardized_estimates(object, ...)"},{"path":"/reference/standardized_estimates.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get standardized estimates — standardized_estimates","text":"object object class modsem_da, modsem_mplus, parTable class data.frame ... Additional arguments passed functions","code":""},{"path":"/reference/standardized_estimates.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Get standardized estimates — standardized_estimates","text":"modsem_da, modsem_mplus objects, interaction term standardized var(xz) = 1. interaction term actual variable model, meaning variance. must therefore calculated parameters model. Assuming normality zero-means, variance calculated var(xz) = var(x) * var(z) + cov(x, z)^2. Thus setting variance interaction term 1 'correct' correlation x z zero. means standardized estimates interaction term different using lavaan, since interaction term actual latent variable model, standardized variance 1.","code":""},{"path":"/reference/summary.html","id":null,"dir":"Reference","previous_headings":"","what":"summary for modsem objects — summary.modsem_da","title":"summary for modsem objects — summary.modsem_da","text":"summary modsem objects summary modsem objects summary modsem objects","code":""},{"path":"/reference/summary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"summary for modsem objects — summary.modsem_da","text":"","code":"# S3 method for class 'modsem_da' summary( object, H0 = TRUE, verbose = TRUE, r.squared = TRUE, adjusted.stat = FALSE, digits = 3, scientific = FALSE, ci = FALSE, standardized = FALSE, loadings = TRUE, regressions = TRUE, covariances = TRUE, intercepts = TRUE, variances = TRUE, var.interaction = FALSE, ... ) # S3 method for class 'modsem_mplus' summary( object, scientific = FALSE, standardize = FALSE, ci = FALSE, digits = 3, loadings = TRUE, regressions = TRUE, covariances = TRUE, intercepts = TRUE, variances = TRUE, ... ) # S3 method for class 'modsem_pi' summary(object, ...)"},{"path":"/reference/summary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"summary for modsem objects — summary.modsem_da","text":"object modsem object summarized H0 null model estimated (used comparison) verbose print progress estimation null model r.squared calculate R-squared adjusted.stat sample size corrected/adjustes AIC BIC reported? digits number digits print scientific print p-values scientific notation ci print confidence intervals standardized print standardized estimates loadings print loadings regressions print regressions covariances print covariances intercepts print intercepts variances print variances var.interaction FALSE (default) variances interaction terms removed (present) ... arguments passed lavaan::summary() standardize standardize estimates","code":""},{"path":"/reference/summary.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"summary for modsem objects — summary.modsem_da","text":"","code":"if (FALSE) { # \\dontrun{ m1 <- \" # Outer Model X =~ x1 + x2 + x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z \" est1 <- modsem(m1, oneInt, \"qml\") summary(est1, ci = TRUE, scientific = TRUE) } # }"},{"path":"/reference/trace_path.html","id":null,"dir":"Reference","previous_headings":"","what":"Estimate formulas for (co-)variance paths using Wright's path tracing rules — trace_path","title":"Estimate formulas for (co-)variance paths using Wright's path tracing rules — trace_path","text":"function estimates path x y using path tracing rules. Note works structural parameters, \"=~\" ignored, unless measurement.model = TRUE. want use measurement model, \"~\" mod column pt.","code":""},{"path":"/reference/trace_path.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Estimate formulas for (co-)variance paths using Wright's path tracing rules — trace_path","text":"","code":"trace_path( pt, x, y, parenthesis = TRUE, missing.cov = FALSE, measurement.model = FALSE, maxlen = 100, ... )"},{"path":"/reference/trace_path.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Estimate formulas for (co-)variance paths using Wright's path tracing rules — trace_path","text":"pt data frame columns lhs, op, rhs, mod, modsemify x Source variable y Destination variable parenthesis TRUE, output enclosed parenthesis missing.cov TRUE, covariances missing model syntax added measurement.model TRUE, function use measurement model maxlen Maximum length path aborting ... Additional arguments passed trace_path","code":""},{"path":"/reference/trace_path.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Estimate formulas for (co-)variance paths using Wright's path tracing rules — trace_path","text":"string estimated path (simplified possible)","code":""},{"path":"/reference/trace_path.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Estimate formulas for (co-)variance paths using Wright's path tracing rules — trace_path","text":"","code":"library(modsem) m1 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' pt <- modsemify(m1) trace_path(pt, x = \"Y\", y = \"Y\", missing.cov = TRUE) # variance of Y #> [1] \"(X~~X * Y~X ^ 2 + 2 * X~~Z * Y~X * Y~Z + Y~Z ^ 2 * Z~~Z + Y~~Y)\""},{"path":"/reference/var_interactions.html","id":null,"dir":"Reference","previous_headings":"","what":"Extract or modify parTable from an estimated model with estimated variances of interaction terms — var_interactions","title":"Extract or modify parTable from an estimated model with estimated variances of interaction terms — var_interactions","text":"Extract modify parTable estimated model estimated variances interaction terms","code":""},{"path":"/reference/var_interactions.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Extract or modify parTable from an estimated model with estimated variances of interaction terms — var_interactions","text":"","code":"var_interactions(object, ...)"},{"path":"/reference/var_interactions.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Extract or modify parTable from an estimated model with estimated variances of interaction terms — var_interactions","text":"object object class modsem_da, modsem_mplus, parTable class data.frame ... Additional arguments passed functions","code":""},{"path":"/reference/vcov_modsem_da.html","id":null,"dir":"Reference","previous_headings":"","what":"Wrapper for vcov — vcov_modsem_da","title":"Wrapper for vcov — vcov_modsem_da","text":"wrapper vcov, used modsem::vcov_modsem_da, since vcov namespace modsem, stats","code":""},{"path":"/reference/vcov_modsem_da.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Wrapper for vcov — vcov_modsem_da","text":"","code":"vcov_modsem_da(object, ...)"},{"path":"/reference/vcov_modsem_da.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Wrapper for vcov — vcov_modsem_da","text":"object fittet model inspect ... additional arguments","code":""}] +[{"path":"/LICENSE.html","id":null,"dir":"","previous_headings":"","what":"MIT License","title":"MIT License","text":"Copyright (c) 2024 modsem authors Permission hereby granted, free charge, person obtaining copy software associated documentation files (“Software”), deal Software without restriction, including without limitation rights use, copy, modify, merge, publish, distribute, sublicense, /sell copies Software, permit persons Software furnished , subject following conditions: copyright notice permission notice shall included copies substantial portions Software. SOFTWARE PROVIDED “”, WITHOUT WARRANTY KIND, EXPRESS IMPLIED, INCLUDING LIMITED WARRANTIES MERCHANTABILITY, FITNESS PARTICULAR PURPOSE NONINFRINGEMENT. EVENT SHALL AUTHORS COPYRIGHT HOLDERS LIABLE CLAIM, DAMAGES LIABILITY, WHETHER ACTION CONTRACT, TORT OTHERWISE, ARISING , CONNECTION SOFTWARE USE DEALINGS SOFTWARE.","code":""},{"path":"/articles/customizing.html","id":"specifying-the-measurement-model","dir":"Articles","previous_headings":"","what":"Specifying The Measurement Model","title":"customizing interaction terms","text":"default, modsem() creates possible combinations different product indicators. However, another common approach match indicators order. example, let’s say interaction laten variables X Z: ‘X =~ x1 + x2’ ‘Z =~ z1 + z2’. default get ‘XZ =~ x1z1 + x1z2 + x2z1 + x2z2’. wanted use matching approach want get ‘XZ =~ x1z1 + x2z2’ instead. achieve can use ‘match = TRUE’ argument.","code":"m2 <- ' # Outer Model X =~ x1 + x2 Y =~ y1 + y2 Z =~ z1 + z2 # Inner model Y ~ X + Z + X:Z ' est2 <- modsem(m2, oneInt, match = TRUE) summary(est2) #> modsem: #> Method = dblcent #> lavaan 0.6-19 ended normally after 41 iterations #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 22 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 11.355 #> Degrees of freedom 14 #> P-value (Chi-square) 0.658 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Latent Variables: #> Estimate Std.Err z-value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.819 0.021 38.127 0.000 #> Y =~ #> y1 1.000 #> y2 0.807 0.010 82.495 0.000 #> Z =~ #> z1 1.000 #> z2 0.836 0.024 35.392 0.000 #> XZ =~ #> x1z1 1.000 #> x2z2 0.645 0.024 26.904 0.000 #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> Y ~ #> X 0.688 0.029 23.366 0.000 #> Z 0.576 0.029 20.173 0.000 #> XZ 0.706 0.032 22.405 0.000 #> #> Covariances: #> Estimate Std.Err z-value P(>|z|) #> .x1z1 ~~ #> .x2z2 0.000 #> X ~~ #> Z 0.202 0.025 8.182 0.000 #> XZ 0.003 0.026 0.119 0.905 #> Z ~~ #> XZ 0.042 0.026 1.621 0.105 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .x1 0.179 0.022 8.029 0.000 #> .x2 0.151 0.015 9.956 0.000 #> .y1 0.184 0.021 8.577 0.000 #> .y2 0.136 0.014 9.663 0.000 #> .z1 0.197 0.025 7.802 0.000 #> .z2 0.138 0.018 7.831 0.000 #> .x1z1 0.319 0.035 9.141 0.000 #> .x2z2 0.244 0.016 15.369 0.000 #> X 0.962 0.042 23.120 0.000 #> .Y 0.964 0.042 23.110 0.000 #> Z 0.987 0.044 22.260 0.000 #> XZ 1.041 0.054 19.441 0.000"},{"path":"/articles/customizing.html","id":"more-complicated-models","dir":"Articles","previous_headings":"","what":"More complicated models","title":"customizing interaction terms","text":"want even control can use get_pi_syntax() get_pi_data() functions, can extract modified syntax data modsem, alter accordingly. can particularly useful cases want estimate model using feature lavaan, isn’t available modsem. example, (yet) syntax ordered- multigroup models isn’t flexible lavaan. Thus can modify auto-generated syntax (altered dataset) modsem suit needs.","code":"m3 <- ' # Outer Model X =~ x1 + x2 Y =~ y1 + y2 Z =~ z1 + z2 # Inner model Y ~ X + Z + X:Z ' syntax <- get_pi_syntax(m3) cat(syntax) #> X =~ x1 #> X =~ x2 #> Y =~ y1 #> Y =~ y2 #> Z =~ z1 #> Z =~ z2 #> Y ~ X #> Y ~ Z #> Y ~ XZ #> XZ =~ 1*x1z1 #> XZ =~ x2z1 #> XZ =~ x1z2 #> XZ =~ x2z2 #> x1z1 ~~ 0*x2z2 #> x1z2 ~~ 0*x2z1 #> x1z1 ~~ x1z2 #> x1z1 ~~ x2z1 #> x1z2 ~~ x2z2 #> x2z1 ~~ x2z2 data <- get_pi_data(m3, oneInt) head(data) #> x1 x2 y1 y2 z1 z2 x1z1 #> 1 2.4345722 1.3578655 1.4526897 0.9560888 0.8184825 1.60708140 -0.4823019 #> 2 0.2472734 0.2723201 0.5496756 0.7115311 3.6649148 2.60983102 -2.2680403 #> 3 -1.3647759 -0.5628205 -0.9835467 -0.6697747 1.7249386 2.10981827 -1.9137416 #> 4 3.0432836 2.2153763 6.4641465 4.7805981 2.5697116 3.26335379 2.9385205 #> 5 2.8148841 2.7029616 2.2860280 2.1457643 0.3467850 0.07164577 -1.4009548 #> 6 -0.5453450 -0.7530642 1.1294876 1.1998472 -0.2362958 0.60252657 1.7465860 #> x2z1 x1z2 x2z2 #> 1 -0.1884837 0.3929380 -0.0730934 #> 2 -2.6637694 -1.2630544 -1.4547433 #> 3 -1.4299711 -2.3329864 -1.7383407 #> 4 1.3971422 3.9837389 1.9273102 #> 5 -1.1495704 -2.2058995 -1.8169042 #> 6 2.2950753 0.7717365 1.0568143"},{"path":"/articles/interaction_two_etas.html","id":"the-problem","dir":"Articles","previous_headings":"","what":"The Problem","title":"interaction effects between endogenous variables","text":"Interaction effects two endogenous (.e., dependent) variables work expect product indicator methods (\"dblcent\", \"rca\", \"ca\", \"uca\"). lms- qml approach however, straight forward. lms- qml approach can (default) handle interaction effects endogenous exogenous (.e., independent) variables, interaction effects two endogenous variables. interaction effect two endogenous variables, equations easily written ‘reduced’ form – meaning normal estimation procedures won’t work.","code":""},{"path":"/articles/interaction_two_etas.html","id":"the-solution","dir":"Articles","previous_headings":"","what":"The Solution","title":"interaction effects between endogenous variables","text":"said, work-around limitations lms- qml-approach. essence, model can split two parts, one linear one non-linear. Basically, can replace covariance matrix used estimation non-linear model, model-implied covariance matrix linear model. Thus can treat endogenous variable exogenous – given can expressed linear model.","code":""},{"path":"/articles/interaction_two_etas.html","id":"example","dir":"Articles","previous_headings":"","what":"Example","title":"interaction effects between endogenous variables","text":"Let’s consider theory planned behaviour (TPB) wish estimate quadratic effect INT BEH (INT:INT). following model: Since INT endogenous variable, quadratic term (.e., interaction effect ) include two endogenous variables. Thus ordinarily able estimate model using lms- qml-approach. However, can split model two parts, one linear one non-linear. INT endogenous variable, can expressed linear model – since affected interaction terms: remove part original model, giving us: now just estimate non-linear model, since INT now exogenous variable. however incorporate structural model INT. address , can make modsem replace covariance matrix (phi) (INT, PBC, ATT, SN) model-implied covariance matrix linear model, whilst estimating models simultaneously. acheive , can use cov.syntax argument modsem:","code":"tpb <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ INT:INT ' tpb_linear <- 'INT ~ PBC + ATT + SN' tpb_nonlinear <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) BEH ~ INT + PBC BEH ~ INT:INT ' est_lms <- modsem(tpb_nonlinear, data = TPB, cov.syntax = tpb_linear, method = \"lms\") #> Warning: It is recommended that you have at least 48 nodes for interaction #> effects between endogenous variables in the lms approach 'nodes = 24' summary(est_lms) #> Estimating null model #> EM: Iteration = 1, LogLik = -28467.33, Change = -28467.332 #> EM: Iteration = 2, LogLik = -28124.48, Change = 342.852 #> EM: Iteration = 3, LogLik = -27825.10, Change = 299.377 #> EM: Iteration = 4, LogLik = -27581.12, Change = 243.980 #> EM: Iteration = 5, LogLik = -27370.69, Change = 210.431 #> EM: Iteration = 6, LogLik = -27175.43, Change = 195.264 #> EM: Iteration = 7, LogLik = -27000.48, Change = 174.946 #> EM: Iteration = 8, LogLik = -26848.56, Change = 151.919 #> EM: Iteration = 9, LogLik = -26711.51, Change = 137.051 #> EM: Iteration = 10, LogLik = -26592.54, Change = 118.968 #> EM: Iteration = 11, LogLik = -26504.04, Change = 88.504 #> EM: Iteration = 12, LogLik = -26466.85, Change = 37.190 #> EM: Iteration = 13, LogLik = -26452.38, Change = 14.465 #> EM: Iteration = 14, LogLik = -26439.05, Change = 13.331 #> EM: Iteration = 15, LogLik = -26430.51, Change = 8.541 #> EM: Iteration = 16, LogLik = -26422.81, Change = 7.698 #> EM: Iteration = 17, LogLik = -26403.89, Change = 18.924 #> EM: Iteration = 18, LogLik = -26402.25, Change = 1.642 #> EM: Iteration = 19, LogLik = -26401.21, Change = 1.037 #> EM: Iteration = 20, LogLik = -26400.26, Change = 0.955 #> EM: Iteration = 21, LogLik = -26399.30, Change = 0.960 #> EM: Iteration = 22, LogLik = -26398.64, Change = 0.658 #> EM: Iteration = 23, LogLik = -26398.02, Change = 0.615 #> EM: Iteration = 24, LogLik = -26397.74, Change = 0.278 #> EM: Iteration = 25, LogLik = -26397.33, Change = 0.420 #> EM: Iteration = 26, LogLik = -26397.20, Change = 0.128 #> EM: Iteration = 27, LogLik = -26396.77, Change = 0.425 #> EM: Iteration = 28, LogLik = -26396.48, Change = 0.292 #> EM: Iteration = 29, LogLik = -26396.34, Change = 0.145 #> EM: Iteration = 30, LogLik = -26396.31, Change = 0.022 #> EM: Iteration = 31, LogLik = -26395.95, Change = 0.365 #> EM: Iteration = 32, LogLik = -26395.73, Change = 0.215 #> EM: Iteration = 33, LogLik = -26395.68, Change = 0.055 #> EM: Iteration = 34, LogLik = -26395.37, Change = 0.304 #> EM: Iteration = 35, LogLik = -26395.30, Change = 0.079 #> EM: Iteration = 36, LogLik = -26395.10, Change = 0.198 #> EM: Iteration = 37, LogLik = -26395.04, Change = 0.057 #> EM: Iteration = 38, LogLik = -26394.99, Change = 0.054 #> EM: Iteration = 39, LogLik = -26394.96, Change = 0.028 #> EM: Iteration = 40, LogLik = -26394.93, Change = 0.031 #> EM: Iteration = 41, LogLik = -26394.91, Change = 0.019 #> EM: Iteration = 42, LogLik = -26394.89, Change = 0.023 #> EM: Iteration = 43, LogLik = -26394.87, Change = 0.015 #> EM: Iteration = 44, LogLik = -26394.85, Change = 0.019 #> EM: Iteration = 45, LogLik = -26394.84, Change = 0.013 #> EM: Iteration = 46, LogLik = -26394.82, Change = 0.018 #> EM: Iteration = 47, LogLik = -26394.81, Change = 0.012 #> EM: Iteration = 48, LogLik = -26394.79, Change = 0.018 #> EM: Iteration = 49, LogLik = -26394.78, Change = 0.013 #> EM: Iteration = 50, LogLik = -26394.76, Change = 0.020 #> EM: Iteration = 51, LogLik = -26394.74, Change = 0.015 #> EM: Iteration = 52, LogLik = -26394.72, Change = 0.028 #> EM: Iteration = 53, LogLik = -26394.69, Change = 0.022 #> EM: Iteration = 54, LogLik = -26394.63, Change = 0.062 #> EM: Iteration = 55, LogLik = -26394.58, Change = 0.057 #> EM: Iteration = 56, LogLik = -26394.29, Change = 0.284 #> EM: Iteration = 57, LogLik = -26394.04, Change = 0.248 #> EM: Iteration = 58, LogLik = -26393.97, Change = 0.075 #> EM: Iteration = 59, LogLik = -26393.73, Change = 0.240 #> EM: Iteration = 60, LogLik = -26393.72, Change = 0.011 #> EM: Iteration = 61, LogLik = -26393.71, Change = 0.013 #> EM: Iteration = 62, LogLik = -26393.70, Change = 0.005 #> EM: Iteration = 63, LogLik = -26393.69, Change = 0.008 #> EM: Iteration = 64, LogLik = -26393.69, Change = 0.003 #> EM: Iteration = 65, LogLik = -26393.68, Change = 0.007 #> EM: Iteration = 66, LogLik = -26393.68, Change = 0.003 #> EM: Iteration = 67, LogLik = -26393.67, Change = 0.007 #> EM: Iteration = 68, LogLik = -26393.67, Change = 0.003 #> EM: Iteration = 69, LogLik = -26393.66, Change = 0.006 #> EM: Iteration = 70, LogLik = -26393.66, Change = 0.002 #> EM: Iteration = 71, LogLik = -26393.66, Change = 0.006 #> EM: Iteration = 72, LogLik = -26393.65, Change = 0.002 #> EM: Iteration = 73, LogLik = -26393.65, Change = 0.005 #> EM: Iteration = 74, LogLik = -26393.65, Change = 0.002 #> EM: Iteration = 75, LogLik = -26393.64, Change = 0.005 #> EM: Iteration = 76, LogLik = -26393.64, Change = 0.002 #> EM: Iteration = 77, LogLik = -26393.63, Change = 0.004 #> EM: Iteration = 78, LogLik = -26393.63, Change = 0.002 #> EM: Iteration = 79, LogLik = -26393.63, Change = 0.004 #> EM: Iteration = 80, LogLik = -26393.63, Change = 0.002 #> EM: Iteration = 81, LogLik = -26393.62, Change = 0.004 #> EM: Iteration = 82, LogLik = -26393.62, Change = 0.002 #> EM: Iteration = 83, LogLik = -26393.62, Change = 0.004 #> EM: Iteration = 84, LogLik = -26393.61, Change = 0.002 #> EM: Iteration = 85, LogLik = -26393.61, Change = 0.003 #> EM: Iteration = 86, LogLik = -26393.61, Change = 0.002 #> EM: Iteration = 87, LogLik = -26393.60, Change = 0.003 #> EM: Iteration = 88, LogLik = -26393.60, Change = 0.003 #> EM: Iteration = 89, LogLik = -26393.60, Change = 0.003 #> EM: Iteration = 90, LogLik = -26393.60, Change = 0.003 #> EM: Iteration = 91, LogLik = -26393.59, Change = 0.003 #> EM: Iteration = 92, LogLik = -26393.59, Change = 0.003 #> EM: Iteration = 93, LogLik = -26393.59, Change = 0.003 #> EM: Iteration = 94, LogLik = -26393.59, Change = 0.003 #> EM: Iteration = 95, LogLik = -26393.58, Change = 0.003 #> EM: Iteration = 96, LogLik = -26393.58, Change = 0.003 #> EM: Iteration = 97, LogLik = -26393.58, Change = 0.002 #> EM: Iteration = 98, LogLik = -26393.58, Change = 0.003 #> EM: Iteration = 99, LogLik = -26393.57, Change = 0.002 #> EM: Iteration = 100, LogLik = -26393.57, Change = 0.003 #> EM: Iteration = 101, LogLik = -26393.57, Change = 0.002 #> EM: Iteration = 102, LogLik = -26393.57, Change = 0.003 #> EM: Iteration = 103, LogLik = -26393.56, Change = 0.002 #> EM: Iteration = 104, LogLik = -26393.56, Change = 0.003 #> EM: Iteration = 105, LogLik = -26393.56, Change = 0.002 #> EM: Iteration = 106, LogLik = -26393.56, Change = 0.003 #> EM: Iteration = 107, LogLik = -26393.55, Change = 0.002 #> EM: Iteration = 108, LogLik = -26393.55, Change = 0.003 #> EM: Iteration = 109, LogLik = -26393.55, Change = 0.002 #> EM: Iteration = 110, LogLik = -26393.55, Change = 0.003 #> EM: Iteration = 111, LogLik = -26393.54, Change = 0.002 #> EM: Iteration = 112, LogLik = -26393.54, Change = 0.003 #> EM: Iteration = 113, LogLik = -26393.54, Change = 0.002 #> EM: Iteration = 114, LogLik = -26393.54, Change = 0.003 #> EM: Iteration = 115, LogLik = -26393.53, Change = 0.002 #> EM: Iteration = 116, LogLik = -26393.53, Change = 0.003 #> EM: Iteration = 117, LogLik = -26393.53, Change = 0.002 #> EM: Iteration = 118, LogLik = -26393.53, Change = 0.003 #> EM: Iteration = 119, LogLik = -26393.53, Change = 0.001 #> EM: Iteration = 120, LogLik = -26393.52, Change = 0.003 #> EM: Iteration = 121, LogLik = -26393.52, Change = 0.001 #> EM: Iteration = 122, LogLik = -26393.52, Change = 0.003 #> EM: Iteration = 123, LogLik = -26393.52, Change = 0.001 #> EM: Iteration = 124, LogLik = -26393.51, Change = 0.003 #> EM: Iteration = 125, LogLik = -26393.51, Change = 0.001 #> EM: Iteration = 126, LogLik = -26393.51, Change = 0.003 #> EM: Iteration = 127, LogLik = -26393.51, Change = 0.001 #> EM: Iteration = 128, LogLik = -26393.51, Change = 0.003 #> EM: Iteration = 129, LogLik = -26393.50, Change = 0.001 #> EM: Iteration = 130, LogLik = -26393.50, Change = 0.003 #> EM: Iteration = 131, LogLik = -26393.50, Change = 0.001 #> EM: Iteration = 132, LogLik = -26393.50, Change = 0.003 #> EM: Iteration = 133, LogLik = -26393.50, Change = 0.001 #> EM: Iteration = 134, LogLik = -26393.49, Change = 0.003 #> EM: Iteration = 135, LogLik = -26393.49, Change = 0.001 #> EM: Iteration = 136, LogLik = -26393.49, Change = 0.003 #> EM: Iteration = 137, LogLik = -26393.49, Change = 0.001 #> EM: Iteration = 138, LogLik = -26393.48, Change = 0.003 #> EM: Iteration = 139, LogLik = -26393.48, Change = 0.001 #> EM: Iteration = 140, LogLik = -26393.48, Change = 0.003 #> EM: Iteration = 141, LogLik = -26393.48, Change = 0.001 #> EM: Iteration = 142, LogLik = -26393.48, Change = 0.003 #> EM: Iteration = 143, LogLik = -26393.48, Change = 0.001 #> EM: Iteration = 144, LogLik = -26393.47, Change = 0.003 #> EM: Iteration = 145, LogLik = -26393.47, Change = 0.001 #> EM: Iteration = 146, LogLik = -26393.47, Change = 0.003 #> EM: Iteration = 147, LogLik = -26393.47, Change = 0.000 #> EM: Iteration = 148, LogLik = -26393.46, Change = 0.003 #> EM: Iteration = 149, LogLik = -26393.46, Change = 0.000 #> EM: Iteration = 150, LogLik = -26393.46, Change = 0.003 #> EM: Iteration = 151, LogLik = -26393.46, Change = 0.000 #> EM: Iteration = 152, LogLik = -26393.46, Change = 0.004 #> EM: Iteration = 153, LogLik = -26393.46, Change = 0.000 #> EM: Iteration = 154, LogLik = -26393.45, Change = 0.004 #> EM: Iteration = 155, LogLik = -26393.45, Change = 0.000 #> EM: Iteration = 156, LogLik = -26393.45, Change = 0.004 #> EM: Iteration = 157, LogLik = -26393.45, Change = 0.000 #> #> modsem (version 1.0.3): #> Estimator LMS #> Optimization method EM-NLMINB #> Number of observations 2000 #> Number of iterations 136 #> Loglikelihood -23781.36 #> Akaike (AIC) 47670.72 #> Bayesian (BIC) 47973.16 #> #> Numerical Integration: #> Points of integration (per dim) 24 #> Dimensions 1 #> Total points of integration 24 #> #> Fit Measures for H0: #> Loglikelihood -26393 #> Akaike (AIC) 52892.89 #> Bayesian (BIC) 53189.74 #> Chi-square 66.72 #> Degrees of Freedom (Chi-square) 82 #> P-value (Chi-square) 0.889 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 2612.09 #> Difference test (D) 5224.18 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> BEH 0.235 #> INT 0.365 #> R-Squared Null-Model (H0): #> BEH 0.210 #> INT 0.367 #> R-Squared Change: #> BEH 0.025 #> INT -0.002 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information expected #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> INT =~ #> int1 1.000 #> int2 0.915 0.015 59.13 0.000 #> int3 0.807 0.015 55.25 0.000 #> ATT =~ #> att1 1.000 #> att2 0.876 0.012 71.52 0.000 #> att3 0.787 0.012 66.56 0.000 #> att4 0.693 0.011 60.51 0.000 #> att5 0.885 0.012 71.68 0.000 #> SN =~ #> sn1 1.000 #> sn2 0.893 0.017 52.63 0.000 #> PBC =~ #> pbc1 1.000 #> pbc2 0.912 0.013 69.17 0.000 #> pbc3 0.801 0.012 66.55 0.000 #> BEH =~ #> b1 1.000 #> b2 0.959 0.030 32.01 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> BEH ~ #> INT 0.196 0.025 7.72 0.000 #> PBC 0.238 0.022 10.66 0.000 #> INT:INT 0.129 0.017 7.43 0.000 #> INT ~ #> PBC 0.218 0.029 7.54 0.000 #> ATT 0.210 0.025 8.32 0.000 #> SN 0.172 0.028 6.25 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> int1 1.005 0.022 46.65 0.000 #> int2 1.004 0.020 50.31 0.000 #> int3 0.998 0.018 54.37 0.000 #> att1 1.007 0.025 40.32 0.000 #> att2 1.001 0.022 45.02 0.000 #> att3 1.011 0.020 49.61 0.000 #> att4 0.994 0.019 53.44 0.000 #> att5 0.986 0.022 43.87 0.000 #> sn1 1.000 0.025 39.96 0.000 #> sn2 1.005 0.022 44.71 0.000 #> pbc1 0.991 0.025 40.38 0.000 #> pbc2 0.979 0.023 42.87 0.000 #> pbc3 0.986 0.020 48.34 0.000 #> b1 0.995 0.024 41.61 0.000 #> b2 1.014 0.022 45.15 0.000 #> BEH 0.000 #> INT 0.000 #> ATT 0.000 #> SN 0.000 #> PBC 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> PBC ~~ #> ATT 0.668 0.079 8.48 0.000 #> SN 0.675 0.054 12.48 0.000 #> ATT ~~ #> SN 0.625 0.029 21.63 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> int1 0.161 0.009 18.33 0.000 #> int2 0.161 0.008 20.89 0.000 #> int3 0.170 0.007 23.48 0.000 #> att1 0.167 0.007 23.23 0.000 #> att2 0.150 0.006 24.81 0.000 #> att3 0.160 0.006 26.51 0.000 #> att4 0.163 0.006 27.46 0.000 #> att5 0.159 0.006 24.85 0.000 #> sn1 0.181 0.015 12.48 0.000 #> sn2 0.155 0.012 13.28 0.000 #> pbc1 0.145 0.008 18.27 0.000 #> pbc2 0.160 0.007 21.74 0.000 #> pbc3 0.154 0.007 23.70 0.000 #> b1 0.185 0.019 9.76 0.000 #> b2 0.136 0.017 7.97 0.000 #> BEH 0.475 0.023 20.47 0.000 #> PBC 0.960 0.037 26.14 0.000 #> ATT 1.000 0.058 17.32 0.000 #> SN 0.968 0.086 11.29 0.000 #> INT 0.481 0.019 24.99 0.000 est_qml <- modsem(tpb_nonlinear, data = TPB, cov.syntax = tpb_linear, method = \"qml\") summary(est_qml) #> Estimating null model #> Starting M-step #> #> modsem (version 1.0.3): #> Estimator QML #> Optimization method NLMINB #> Number of observations 2000 #> Number of iterations 76 #> Loglikelihood -26360.52 #> Akaike (AIC) 52829.04 #> Bayesian (BIC) 53131.49 #> #> Fit Measures for H0: #> Loglikelihood -26393 #> Akaike (AIC) 52892.45 #> Bayesian (BIC) 53189.29 #> Chi-square 66.27 #> Degrees of Freedom (Chi-square) 82 #> P-value (Chi-square) 0.897 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 32.70 #> Difference test (D) 65.41 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> BEH 0.239 #> INT 0.370 #> R-Squared Null-Model (H0): #> BEH 0.210 #> INT 0.367 #> R-Squared Change: #> BEH 0.029 #> INT 0.003 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information observed #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> INT =~ #> int1 1.000 #> int2 0.914 0.015 59.04 0.000 #> int3 0.807 0.015 55.65 0.000 #> ATT =~ #> att1 1.000 #> att2 0.878 0.012 71.56 0.000 #> att3 0.789 0.012 66.37 0.000 #> att4 0.695 0.011 61.00 0.000 #> att5 0.887 0.013 70.85 0.000 #> SN =~ #> sn1 1.000 #> sn2 0.888 0.017 52.62 0.000 #> PBC =~ #> pbc1 1.000 #> pbc2 0.913 0.013 69.38 0.000 #> pbc3 0.801 0.012 66.08 0.000 #> BEH =~ #> b1 1.000 #> b2 0.960 0.032 29.91 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> BEH ~ #> INT 0.197 0.025 7.76 0.000 #> PBC 0.239 0.023 10.59 0.000 #> INT:INT 0.128 0.016 7.88 0.000 #> INT ~ #> PBC 0.222 0.030 7.51 0.000 #> ATT 0.213 0.026 8.17 0.000 #> SN 0.175 0.028 6.33 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> int1 1.014 0.022 46.96 0.000 #> int2 1.012 0.020 50.41 0.000 #> int3 1.005 0.018 54.80 0.000 #> att1 1.014 0.024 42.01 0.000 #> att2 1.007 0.021 46.97 0.000 #> att3 1.016 0.020 51.45 0.000 #> att4 0.999 0.018 55.65 0.000 #> att5 0.992 0.022 45.67 0.000 #> sn1 1.006 0.024 41.66 0.000 #> sn2 1.010 0.022 46.71 0.000 #> pbc1 0.998 0.024 42.41 0.000 #> pbc2 0.985 0.022 44.93 0.000 #> pbc3 0.991 0.020 50.45 0.000 #> b1 0.999 0.023 42.64 0.000 #> b2 1.017 0.022 46.25 0.000 #> BEH 0.000 #> INT 0.000 #> ATT 0.000 #> SN 0.000 #> PBC 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> PBC ~~ #> ATT 0.678 0.029 23.45 0.000 #> SN 0.678 0.029 23.08 0.000 #> ATT ~~ #> SN 0.629 0.029 21.70 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> int1 0.158 0.009 18.22 0.000 #> int2 0.160 0.008 20.38 0.000 #> int3 0.168 0.007 23.63 0.000 #> att1 0.167 0.007 23.53 0.000 #> att2 0.150 0.006 24.71 0.000 #> att3 0.160 0.006 26.38 0.000 #> att4 0.162 0.006 27.64 0.000 #> att5 0.159 0.006 24.93 0.000 #> sn1 0.178 0.015 12.09 0.000 #> sn2 0.157 0.012 13.26 0.000 #> pbc1 0.145 0.008 18.44 0.000 #> pbc2 0.160 0.007 21.42 0.000 #> pbc3 0.154 0.006 23.80 0.000 #> b1 0.185 0.020 9.42 0.000 #> b2 0.135 0.018 7.60 0.000 #> BEH 0.475 0.024 19.74 0.000 #> PBC 0.962 0.036 27.04 0.000 #> ATT 0.998 0.037 26.93 0.000 #> SN 0.988 0.039 25.23 0.000 #> INT 0.488 0.020 24.59 0.000"},{"path":"/articles/lms_qml.html","id":"the-latent-moderated-structural-equations-lms-and-the-quasi-maximum-likelihood-qml-approach","dir":"Articles","previous_headings":"","what":"The Latent Moderated Structural Equations (LMS) and the Quasi Maximum Likelihood (QML) approach","title":"LMS and QML approaches","text":"LMS- QML approach works models, interaction effects endogenous can bit tricky estimate (see vignette. approaches (particularily LMS approach) quite computationally intensive, thus partly implemented C++ (using Rcpp RcppArmadillo). Additionally starting parameters estimated using double centering approach (means observed variables) used generate good starting parameters faster convergence. want see progress estimation process can use ´verbose = TRUE´.","code":""},{"path":"/articles/lms_qml.html","id":"a-simple-example","dir":"Articles","previous_headings":"The Latent Moderated Structural Equations (LMS) and the Quasi Maximum Likelihood (QML) approach","what":"A Simple Example","title":"LMS and QML approaches","text":"can see example LMS approach simple model. default summary function calculates fit measures compared null model (.e., model without interaction term). can see example using QML approach.","code":"library(modsem) m1 <- ' # Outer Model X =~ x1 X =~ x2 + x3 Z =~ z1 + z2 + z3 Y =~ y1 + y2 + y3 # Inner model Y ~ X + Z Y ~ X:Z ' lms1 <- modsem(m1, oneInt, method = \"lms\") summary(lms1, standardized = TRUE) # standardized estimates #> Estimating null model #> EM: Iteration = 1, LogLik = -17831.87, Change = -17831.875 #> EM: Iteration = 2, LogLik = -17831.87, Change = 0.000 #> #> modsem (version 1.0.3): #> Estimator LMS #> Optimization method EM-NLMINB #> Number of observations 2000 #> Number of iterations 92 #> Loglikelihood -14687.85 #> Akaike (AIC) 29437.71 #> Bayesian (BIC) 29611.34 #> #> Numerical Integration: #> Points of integration (per dim) 24 #> Dimensions 1 #> Total points of integration 24 #> #> Fit Measures for H0: #> Loglikelihood -17832 #> Akaike (AIC) 35723.75 #> Bayesian (BIC) 35891.78 #> Chi-square 17.52 #> Degrees of Freedom (Chi-square) 24 #> P-value (Chi-square) 0.826 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 3144.02 #> Difference test (D) 6288.04 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> Y 0.596 #> R-Squared Null-Model (H0): #> Y 0.395 #> R-Squared Change: #> Y 0.201 #> #> Parameter Estimates: #> Coefficients standardized #> Information expected #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> X =~ #> x1 0.926 #> x2 0.891 0.014 65.27 0.000 #> x3 0.912 0.013 68.77 0.000 #> Z =~ #> z1 0.927 #> z2 0.898 0.014 65.55 0.000 #> z3 0.913 0.013 69.05 0.000 #> Y =~ #> y1 0.969 #> y2 0.954 0.009 106.30 0.000 #> y3 0.961 0.009 112.47 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> Y ~ #> X 0.427 0.020 20.89 0.000 #> Z 0.370 0.019 19.53 0.000 #> X:Z 0.454 0.017 26.72 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> X ~~ #> Z 0.199 0.027 7.29 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> x1 0.142 0.007 19.63 0.000 #> x2 0.206 0.009 24.10 0.000 #> x3 0.169 0.008 21.53 0.000 #> z1 0.141 0.008 18.74 0.000 #> z2 0.193 0.009 22.64 0.000 #> z3 0.167 0.008 20.78 0.000 #> y1 0.061 0.003 17.98 0.000 #> y2 0.090 0.004 22.74 0.000 #> y3 0.077 0.004 20.73 0.000 #> X 1.000 0.016 60.80 0.000 #> Z 1.000 0.018 54.92 0.000 #> Y 0.404 0.015 27.12 0.000 qml1 <- modsem(m1, oneInt, method = \"qml\") summary(qml1) #> Estimating null model #> Starting M-step #> #> modsem (version 1.0.3): #> Estimator QML #> Optimization method NLMINB #> Number of observations 2000 #> Number of iterations 111 #> Loglikelihood -17496.22 #> Akaike (AIC) 35054.43 #> Bayesian (BIC) 35228.06 #> #> Fit Measures for H0: #> Loglikelihood -17832 #> Akaike (AIC) 35723.75 #> Bayesian (BIC) 35891.78 #> Chi-square 17.52 #> Degrees of Freedom (Chi-square) 24 #> P-value (Chi-square) 0.826 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 335.66 #> Difference test (D) 671.32 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> Y 0.607 #> R-Squared Null-Model (H0): #> Y 0.395 #> R-Squared Change: #> Y 0.211 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information observed #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.803 0.013 63.96 0.000 #> x3 0.914 0.013 67.80 0.000 #> Z =~ #> z1 1.000 #> z2 0.810 0.012 65.12 0.000 #> z3 0.881 0.013 67.62 0.000 #> Y =~ #> y1 1.000 #> y2 0.798 0.007 107.57 0.000 #> y3 0.899 0.008 112.55 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> Y ~ #> X 0.674 0.032 20.94 0.000 #> Z 0.566 0.030 18.96 0.000 #> X:Z 0.712 0.028 25.45 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> x1 1.023 0.024 42.89 0.000 #> x2 1.215 0.020 60.99 0.000 #> x3 0.919 0.022 41.48 0.000 #> z1 1.012 0.024 41.57 0.000 #> z2 1.206 0.020 59.27 0.000 #> z3 0.916 0.022 42.06 0.000 #> y1 1.038 0.033 31.45 0.000 #> y2 1.221 0.027 45.49 0.000 #> y3 0.955 0.030 31.86 0.000 #> Y 0.000 #> X 0.000 #> Z 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> X ~~ #> Z 0.200 0.024 8.24 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> x1 0.158 0.009 18.14 0.000 #> x2 0.162 0.007 23.19 0.000 #> x3 0.165 0.008 20.82 0.000 #> z1 0.166 0.009 18.34 0.000 #> z2 0.159 0.007 22.62 0.000 #> z3 0.158 0.008 20.71 0.000 #> y1 0.159 0.009 17.98 0.000 #> y2 0.154 0.007 22.67 0.000 #> y3 0.164 0.008 20.71 0.000 #> X 0.983 0.036 26.99 0.000 #> Z 1.019 0.038 26.95 0.000 #> Y 0.943 0.038 24.87 0.000"},{"path":"/articles/lms_qml.html","id":"a-more-complicated-example","dir":"Articles","previous_headings":"The Latent Moderated Structural Equations (LMS) and the Quasi Maximum Likelihood (QML) approach","what":"A more complicated example","title":"LMS and QML approaches","text":"can see example complicated example using model theory planned behaviour (TPB), two endogenous variables, interaction endogenous exogenous variable. estimating complicated models LMS-approach, recommended increase number nodes used numerical integration. default number nodes set 16, can increased using nodes argument. argument effect QML approach. interaction effect endogenous exogenous variable, recommended use least 32 nodes LMS-approach. can also get robust standard errors setting robust.se = TRUE modsem() function. Note: want lms-approach give similar results possible mplus, increase number nodes (e.g., nodes = 100).","code":"# ATT = Attitude, # PBC = Perceived Behavioural Control # INT = Intention # SN = Subjective Norms # BEH = Behaviour tpb <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ INT:PBC ' lms2 <- modsem(tpb, TPB, method = \"lms\", nodes = 32) summary(lms2) #> Estimating null model #> EM: Iteration = 1, LogLik = -26393.22, Change = -26393.223 #> EM: Iteration = 2, LogLik = -26393.22, Change = 0.000 #> #> modsem (version 1.0.3): #> Estimator LMS #> Optimization method EM-NLMINB #> Number of observations 2000 #> Number of iterations 70 #> Loglikelihood -23439.02 #> Akaike (AIC) 46986.04 #> Bayesian (BIC) 47288.49 #> #> Numerical Integration: #> Points of integration (per dim) 32 #> Dimensions 1 #> Total points of integration 32 #> #> Fit Measures for H0: #> Loglikelihood -26393 #> Akaike (AIC) 52892.45 #> Bayesian (BIC) 53189.29 #> Chi-square 66.27 #> Degrees of Freedom (Chi-square) 82 #> P-value (Chi-square) 0.897 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 2954.20 #> Difference test (D) 5908.41 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> INT 0.364 #> BEH 0.259 #> R-Squared Null-Model (H0): #> INT 0.367 #> BEH 0.210 #> R-Squared Change: #> INT -0.003 #> BEH 0.049 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information expected #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> PBC =~ #> pbc1 1.000 #> pbc2 0.914 0.013 69.02 0.000 #> pbc3 0.802 0.012 65.40 0.000 #> ATT =~ #> att1 1.000 #> att2 0.878 0.012 70.82 0.000 #> att3 0.789 0.012 65.78 0.000 #> att4 0.695 0.011 61.10 0.000 #> att5 0.887 0.013 70.28 0.000 #> SN =~ #> sn1 1.000 #> sn2 0.889 0.017 52.14 0.000 #> INT =~ #> int1 1.000 #> int2 0.913 0.015 58.98 0.000 #> int3 0.807 0.014 55.84 0.000 #> BEH =~ #> b1 1.000 #> b2 0.959 0.030 31.77 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> INT ~ #> PBC 0.218 0.030 7.32 0.000 #> ATT 0.214 0.026 8.18 0.000 #> SN 0.176 0.027 6.42 0.000 #> BEH ~ #> PBC 0.233 0.023 10.24 0.000 #> INT 0.188 0.025 7.59 0.000 #> PBC:INT 0.205 0.019 11.04 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> pbc1 0.990 0.023 43.17 0.000 #> pbc2 0.978 0.021 45.79 0.000 #> pbc3 0.985 0.019 51.31 0.000 #> att1 1.009 0.024 41.46 0.000 #> att2 1.002 0.022 46.30 0.000 #> att3 1.012 0.020 51.24 0.000 #> att4 0.995 0.018 55.01 0.000 #> att5 0.988 0.022 44.94 0.000 #> sn1 1.001 0.024 40.93 0.000 #> sn2 1.006 0.022 46.05 0.000 #> int1 1.010 0.022 44.93 0.000 #> int2 1.009 0.021 48.14 0.000 #> int3 1.002 0.019 52.81 0.000 #> b1 0.999 0.022 45.57 0.000 #> b2 1.017 0.021 49.38 0.000 #> INT 0.000 #> BEH 0.000 #> PBC 0.000 #> ATT 0.000 #> SN 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> PBC ~~ #> ATT 0.668 0.021 31.56 0.000 #> SN 0.668 0.022 30.34 0.000 #> ATT ~~ #> SN 0.623 0.019 32.86 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> pbc1 0.148 0.008 18.92 0.000 #> pbc2 0.159 0.007 21.70 0.000 #> pbc3 0.155 0.007 23.70 0.000 #> att1 0.167 0.007 23.64 0.000 #> att2 0.150 0.006 24.73 0.000 #> att3 0.159 0.006 26.68 0.000 #> att4 0.162 0.006 27.71 0.000 #> att5 0.159 0.006 25.12 0.000 #> sn1 0.178 0.015 11.99 0.000 #> sn2 0.156 0.012 13.23 0.000 #> int1 0.157 0.009 18.36 0.000 #> int2 0.160 0.008 20.57 0.000 #> int3 0.168 0.007 24.33 0.000 #> b1 0.185 0.019 9.96 0.000 #> b2 0.136 0.017 8.13 0.000 #> PBC 0.947 0.017 54.56 0.000 #> ATT 0.992 0.014 69.78 0.000 #> SN 0.981 0.015 64.38 0.000 #> INT 0.491 0.020 25.00 0.000 #> BEH 0.456 0.023 20.13 0.000 qml2 <- modsem(tpb, TPB, method = \"qml\") summary(qml2, standardized = TRUE) # standardized estimates #> Estimating null model #> Starting M-step #> #> modsem (version 1.0.3): #> Estimator QML #> Optimization method NLMINB #> Number of observations 2000 #> Number of iterations 73 #> Loglikelihood -26326.25 #> Akaike (AIC) 52760.5 #> Bayesian (BIC) 53062.95 #> #> Fit Measures for H0: #> Loglikelihood -26393 #> Akaike (AIC) 52892.45 #> Bayesian (BIC) 53189.29 #> Chi-square 66.27 #> Degrees of Freedom (Chi-square) 82 #> P-value (Chi-square) 0.897 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 66.97 #> Difference test (D) 133.95 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> INT 0.366 #> BEH 0.263 #> R-Squared Null-Model (H0): #> INT 0.367 #> BEH 0.210 #> R-Squared Change: #> INT 0.000 #> BEH 0.053 #> #> Parameter Estimates: #> Coefficients standardized #> Information observed #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> PBC =~ #> pbc1 0.933 #> pbc2 0.913 0.013 69.47 0.000 #> pbc3 0.894 0.014 66.10 0.000 #> ATT =~ #> att1 0.925 #> att2 0.915 0.013 71.56 0.000 #> att3 0.892 0.013 66.38 0.000 #> att4 0.865 0.014 61.00 0.000 #> att5 0.912 0.013 70.85 0.000 #> SN =~ #> sn1 0.921 #> sn2 0.913 0.017 52.61 0.000 #> INT =~ #> int1 0.912 #> int2 0.895 0.015 59.05 0.000 #> int3 0.866 0.016 55.73 0.000 #> BEH =~ #> b1 0.877 #> b2 0.900 0.028 31.71 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> INT ~ #> PBC 0.243 0.033 7.35 0.000 #> ATT 0.242 0.030 8.16 0.000 #> SN 0.199 0.031 6.37 0.000 #> BEH ~ #> PBC 0.289 0.028 10.37 0.000 #> INT 0.212 0.028 7.69 0.000 #> PBC:INT 0.227 0.020 11.32 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> PBC ~~ #> ATT 0.692 0.030 23.45 0.000 #> SN 0.695 0.030 23.08 0.000 #> ATT ~~ #> SN 0.634 0.029 21.70 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> pbc1 0.130 0.007 18.39 0.000 #> pbc2 0.166 0.008 21.43 0.000 #> pbc3 0.201 0.008 23.89 0.000 #> att1 0.144 0.006 23.53 0.000 #> att2 0.164 0.007 24.71 0.000 #> att3 0.204 0.008 26.38 0.000 #> att4 0.252 0.009 27.65 0.000 #> att5 0.168 0.007 24.93 0.000 #> sn1 0.153 0.013 12.09 0.000 #> sn2 0.167 0.013 13.26 0.000 #> int1 0.168 0.009 18.11 0.000 #> int2 0.199 0.010 20.41 0.000 #> int3 0.249 0.011 23.55 0.000 #> b1 0.231 0.023 10.12 0.000 #> b2 0.191 0.024 8.10 0.000 #> PBC 1.000 0.037 27.07 0.000 #> ATT 1.000 0.037 26.93 0.000 #> SN 1.000 0.040 25.22 0.000 #> INT 0.634 0.026 24.64 0.000 #> BEH 0.737 0.037 20.17 0.000"},{"path":"/articles/modsem.html","id":"the-basic-syntax","dir":"Articles","previous_headings":"","what":"The Basic Syntax","title":"modsem","text":"modsem basically introduces new feature lavaan-syntax – semicolon operator (“:”). semicolon operator works way lm()-function. order specify interaction effect two variables, join Var1:Var2, Models can either estimated using one product indicator approaches (“ca”, “rca”, “dblcent”, “pind”) using latent moderated structural equations approach (“lms”), quasi maximum likelihood approach (“qml”). product indicator approaches estimated via lavaan, whilst lms qml approaches estimated via modsem .","code":""},{"path":"/articles/modsem.html","id":"a-simple-example","dir":"Articles","previous_headings":"The Basic Syntax","what":"A Simple Example","title":"modsem","text":"can see simple example specify interaction effect two latent variables lavaan. default model estimated using “dblcent” method. want use another method, method can changed using method argument.","code":"m1 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' est1 <- modsem(m1, oneInt) summary(est1) #> modsem: #> Method = dblcent #> lavaan 0.6-19 ended normally after 159 iterations #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 60 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 122.924 #> Degrees of freedom 111 #> P-value (Chi-square) 0.207 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Latent Variables: #> Estimate Std.Err z-value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.804 0.013 63.612 0.000 #> x3 0.916 0.014 67.144 0.000 #> Y =~ #> y1 1.000 #> y2 0.798 0.007 107.428 0.000 #> y3 0.899 0.008 112.453 0.000 #> Z =~ #> z1 1.000 #> z2 0.812 0.013 64.763 0.000 #> z3 0.882 0.013 67.014 0.000 #> XZ =~ #> x1z1 1.000 #> x2z1 0.805 0.013 60.636 0.000 #> x3z1 0.877 0.014 62.680 0.000 #> x1z2 0.793 0.013 59.343 0.000 #> x2z2 0.646 0.015 43.672 0.000 #> x3z2 0.706 0.016 44.292 0.000 #> x1z3 0.887 0.014 63.700 0.000 #> x2z3 0.716 0.016 45.645 0.000 #> x3z3 0.781 0.017 45.339 0.000 #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> Y ~ #> X 0.675 0.027 25.379 0.000 #> Z 0.561 0.026 21.606 0.000 #> XZ 0.702 0.027 26.360 0.000 #> #> Covariances: #> Estimate Std.Err z-value P(>|z|) #> .x1z1 ~~ #> .x2z2 0.000 #> .x2z3 0.000 #> .x3z2 0.000 #> .x3z3 0.000 #> .x2z1 ~~ #> .x1z2 0.000 #> .x1z2 ~~ #> .x2z3 0.000 #> .x3z1 ~~ #> .x1z2 0.000 #> .x1z2 ~~ #> .x3z3 0.000 #> .x2z1 ~~ #> .x1z3 0.000 #> .x2z2 ~~ #> .x1z3 0.000 #> .x3z1 ~~ #> .x1z3 0.000 #> .x3z2 ~~ #> .x1z3 0.000 #> .x2z1 ~~ #> .x3z2 0.000 #> .x3z3 0.000 #> .x3z1 ~~ #> .x2z2 0.000 #> .x2z2 ~~ #> .x3z3 0.000 #> .x3z1 ~~ #> .x2z3 0.000 #> .x3z2 ~~ #> .x2z3 0.000 #> .x1z1 ~~ #> .x1z2 0.115 0.008 14.802 0.000 #> .x1z3 0.114 0.008 13.947 0.000 #> .x2z1 0.125 0.008 16.095 0.000 #> .x3z1 0.140 0.009 16.135 0.000 #> .x1z2 ~~ #> .x1z3 0.103 0.007 14.675 0.000 #> .x2z2 0.128 0.006 20.850 0.000 #> .x3z2 0.146 0.007 21.243 0.000 #> .x1z3 ~~ #> .x2z3 0.116 0.007 17.818 0.000 #> .x3z3 0.135 0.007 18.335 0.000 #> .x2z1 ~~ #> .x2z2 0.135 0.006 20.905 0.000 #> .x2z3 0.145 0.007 21.145 0.000 #> .x3z1 0.114 0.007 16.058 0.000 #> .x2z2 ~~ #> .x2z3 0.117 0.006 20.419 0.000 #> .x3z2 0.116 0.006 20.586 0.000 #> .x2z3 ~~ #> .x3z3 0.109 0.006 18.059 0.000 #> .x3z1 ~~ #> .x3z2 0.138 0.007 19.331 0.000 #> .x3z3 0.158 0.008 20.269 0.000 #> .x3z2 ~~ #> .x3z3 0.131 0.007 19.958 0.000 #> X ~~ #> Z 0.201 0.024 8.271 0.000 #> XZ 0.016 0.025 0.628 0.530 #> Z ~~ #> XZ 0.062 0.025 2.449 0.014 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .x1 0.160 0.009 17.871 0.000 #> .x2 0.162 0.007 22.969 0.000 #> .x3 0.163 0.008 20.161 0.000 #> .y1 0.159 0.009 17.896 0.000 #> .y2 0.154 0.007 22.640 0.000 #> .y3 0.164 0.008 20.698 0.000 #> .z1 0.168 0.009 18.143 0.000 #> .z2 0.158 0.007 22.264 0.000 #> .z3 0.158 0.008 20.389 0.000 #> .x1z1 0.311 0.014 22.227 0.000 #> .x2z1 0.292 0.011 27.287 0.000 #> .x3z1 0.327 0.012 26.275 0.000 #> .x1z2 0.290 0.011 26.910 0.000 #> .x2z2 0.239 0.008 29.770 0.000 #> .x3z2 0.270 0.009 29.117 0.000 #> .x1z3 0.272 0.012 23.586 0.000 #> .x2z3 0.245 0.009 27.979 0.000 #> .x3z3 0.297 0.011 28.154 0.000 #> X 0.981 0.036 26.895 0.000 #> .Y 0.990 0.038 25.926 0.000 #> Z 1.016 0.038 26.856 0.000 #> XZ 1.045 0.044 24.004 0.000 est1 <- modsem(m1, oneInt, method = \"lms\") summary(est1) #> Estimating null model #> EM: Iteration = 1, LogLik = -17831.87, Change = -17831.875 #> EM: Iteration = 2, LogLik = -17831.87, Change = 0.000 #> #> modsem (version 1.0.3): #> Estimator LMS #> Optimization method EM-NLMINB #> Number of observations 2000 #> Number of iterations 92 #> Loglikelihood -14687.85 #> Akaike (AIC) 29437.71 #> Bayesian (BIC) 29611.34 #> #> Numerical Integration: #> Points of integration (per dim) 24 #> Dimensions 1 #> Total points of integration 24 #> #> Fit Measures for H0: #> Loglikelihood -17832 #> Akaike (AIC) 35723.75 #> Bayesian (BIC) 35891.78 #> Chi-square 17.52 #> Degrees of Freedom (Chi-square) 24 #> P-value (Chi-square) 0.826 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 3144.02 #> Difference test (D) 6288.04 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> Y 0.596 #> R-Squared Null-Model (H0): #> Y 0.395 #> R-Squared Change: #> Y 0.201 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information expected #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.804 0.012 65.27 0.000 #> x3 0.915 0.013 68.77 0.000 #> Z =~ #> z1 1.000 #> z2 0.810 0.012 65.55 0.000 #> z3 0.881 0.013 69.05 0.000 #> Y =~ #> y1 1.000 #> y2 0.799 0.008 106.30 0.000 #> y3 0.899 0.008 112.47 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> Y ~ #> X 0.676 0.032 20.89 0.000 #> Z 0.572 0.029 19.53 0.000 #> X:Z 0.712 0.027 26.72 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> x1 1.025 0.021 48.95 0.000 #> x2 1.218 0.018 68.87 0.000 #> x3 0.922 0.020 47.18 0.000 #> z1 1.016 0.028 36.17 0.000 #> z2 1.209 0.023 51.86 0.000 #> z3 0.920 0.025 36.75 0.000 #> y1 1.046 0.035 29.91 0.000 #> y2 1.227 0.029 42.98 0.000 #> y3 0.962 0.032 30.17 0.000 #> Y 0.000 #> X 0.000 #> Z 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> X ~~ #> Z 0.198 0.027 7.29 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> x1 0.160 0.008 19.63 0.000 #> x2 0.163 0.007 24.10 0.000 #> x3 0.165 0.008 21.53 0.000 #> z1 0.166 0.009 18.74 0.000 #> z2 0.160 0.007 22.64 0.000 #> z3 0.158 0.008 20.78 0.000 #> y1 0.160 0.009 17.98 0.000 #> y2 0.154 0.007 22.74 0.000 #> y3 0.163 0.008 20.73 0.000 #> X 0.972 0.016 60.80 0.000 #> Z 1.017 0.019 54.92 0.000 #> Y 0.984 0.036 27.12 0.000"},{"path":"/articles/modsem.html","id":"interactions-between-two-observed-variables","dir":"Articles","previous_headings":"The Basic Syntax","what":"Interactions Between two Observed Variables","title":"modsem","text":"modsem allow estimate interactions latent variables, also interactions observed variables. first run regression observed variables, interaction x1 z2, run equivalent model using modsem(). Regression Using modsem() general, interactions observed variables recommended use method = “pind”. Interaction effects observed variables supported LMS- QML-approach. certain circumstances, can define latent variabale single indicator estimate interaction effect two observed variables, LMS QML approach, generally recommended.","code":"reg1 <- lm(y1 ~ x1*z1, oneInt) summary(reg1) #> #> Call: #> lm(formula = y1 ~ x1 * z1, data = oneInt) #> #> Residuals: #> Min 1Q Median 3Q Max #> -3.7155 -0.8087 -0.0367 0.8078 4.6531 #> #> Coefficients: #> Estimate Std. Error t value Pr(>|t|) #> (Intercept) 0.51422 0.04618 11.135 <2e-16 *** #> x1 0.05477 0.03387 1.617 0.1060 #> z1 -0.06575 0.03461 -1.900 0.0576 . #> x1:z1 0.54361 0.02272 23.926 <2e-16 *** #> --- #> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 #> #> Residual standard error: 1.184 on 1996 degrees of freedom #> Multiple R-squared: 0.4714, Adjusted R-squared: 0.4706 #> F-statistic: 593.3 on 3 and 1996 DF, p-value: < 2.2e-16 # Here we use \"pind\" as the method (see chapter 3) est2 <- modsem('y1 ~ x1 + z1 + x1:z1', data = oneInt, method = \"pind\") summary(est2) #> modsem: #> Method = pind #> lavaan 0.6-19 ended normally after 1 iteration #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 4 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 0.000 #> Degrees of freedom 0 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> y1 ~ #> x1 0.055 0.034 1.619 0.105 #> z1 -0.066 0.035 -1.902 0.057 #> x1z1 0.544 0.023 23.950 0.000 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .y1 1.399 0.044 31.623 0.000"},{"path":"/articles/modsem.html","id":"interactions-between-latent-and-observed-variables","dir":"Articles","previous_headings":"The Basic Syntax","what":"Interactions between Latent and Observed Variables","title":"modsem","text":"modsem also allows estimate interaction effects latent observed variables. , just join latent observed variable colon, e.g., ‘latent:observer’. interactions observed variables, generally recommended use method = “pind” estimating effect observed x latent","code":"m3 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 # Inner model Y ~ X + z1 + X:z1 ' est3 <- modsem(m3, oneInt, method = \"pind\") summary(est3) #> modsem: #> Method = pind #> lavaan 0.6-19 ended normally after 45 iterations #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 22 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 4468.171 #> Degrees of freedom 32 #> P-value (Chi-square) 0.000 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Latent Variables: #> Estimate Std.Err z-value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.803 0.013 63.697 0.000 #> x3 0.915 0.014 67.548 0.000 #> Y =~ #> y1 1.000 #> y2 0.798 0.007 115.375 0.000 #> y3 0.899 0.007 120.783 0.000 #> Xz1 =~ #> x1z1 1.000 #> x2z1 0.947 0.010 96.034 0.000 #> x3z1 0.902 0.009 99.512 0.000 #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> Y ~ #> X 0.021 0.034 0.614 0.540 #> z1 -0.185 0.023 -8.096 0.000 #> Xz1 0.646 0.017 37.126 0.000 #> #> Covariances: #> Estimate Std.Err z-value P(>|z|) #> X ~~ #> Xz1 1.243 0.055 22.523 0.000 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .x1 0.158 0.009 17.976 0.000 #> .x2 0.164 0.007 23.216 0.000 #> .x3 0.162 0.008 20.325 0.000 #> .y1 0.158 0.009 17.819 0.000 #> .y2 0.154 0.007 22.651 0.000 #> .y3 0.164 0.008 20.744 0.000 #> .x1z1 0.315 0.017 18.328 0.000 #> .x2z1 0.428 0.019 22.853 0.000 #> .x3z1 0.337 0.016 21.430 0.000 #> X 0.982 0.036 26.947 0.000 #> .Y 1.112 0.040 27.710 0.000 #> Xz1 3.965 0.136 29.217 0.000"},{"path":"/articles/modsem.html","id":"quadratic-effects","dir":"Articles","previous_headings":"The Basic Syntax","what":"Quadratic Effects","title":"modsem","text":"essence, quadratic effects just special case interaction effects. Thus modsem can also used estimate quadratic effects.","code":"m4 <- ' # Outer Model X =~ x1 + x2 + x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + Z:X + X:X ' est4 <- modsem(m4, oneInt, \"qml\") summary(est4) #> Estimating null model #> Starting M-step #> #> modsem (version 1.0.3): #> Estimator QML #> Optimization method NLMINB #> Number of observations 2000 #> Number of iterations 123 #> Loglikelihood -17496.2 #> Akaike (AIC) 35056.4 #> Bayesian (BIC) 35235.63 #> #> Fit Measures for H0: #> Loglikelihood -17832 #> Akaike (AIC) 35723.75 #> Bayesian (BIC) 35891.78 #> Chi-square 17.52 #> Degrees of Freedom (Chi-square) 24 #> P-value (Chi-square) 0.826 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 335.68 #> Difference test (D) 671.35 #> Degrees of freedom (D) 2 #> P-value (D) 0.000 #> #> R-Squared: #> Y 0.607 #> R-Squared Null-Model (H0): #> Y 0.395 #> R-Squared Change: #> Y 0.212 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information observed #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.803 0.013 63.961 0.000 #> x3 0.914 0.013 67.797 0.000 #> Z =~ #> z1 1.000 #> z2 0.810 0.012 65.124 0.000 #> z3 0.881 0.013 67.621 0.000 #> Y =~ #> y1 1.000 #> y2 0.798 0.007 107.567 0.000 #> y3 0.899 0.008 112.542 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> Y ~ #> X 0.674 0.032 20.888 0.000 #> Z 0.566 0.030 18.948 0.000 #> X:X -0.005 0.023 -0.207 0.836 #> X:Z 0.713 0.029 24.554 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> x1 1.023 0.024 42.894 0.000 #> x2 1.216 0.020 60.996 0.000 #> x3 0.919 0.022 41.484 0.000 #> z1 1.012 0.024 41.576 0.000 #> z2 1.206 0.020 59.271 0.000 #> z3 0.916 0.022 42.063 0.000 #> y1 1.042 0.038 27.684 0.000 #> y2 1.224 0.030 40.159 0.000 #> y3 0.958 0.034 28.101 0.000 #> Y 0.000 #> X 0.000 #> Z 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> X ~~ #> Z 0.200 0.024 8.239 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> x1 0.158 0.009 18.145 0.000 #> x2 0.162 0.007 23.188 0.000 #> x3 0.165 0.008 20.821 0.000 #> z1 0.166 0.009 18.341 0.000 #> z2 0.159 0.007 22.622 0.000 #> z3 0.158 0.008 20.714 0.000 #> y1 0.159 0.009 17.975 0.000 #> y2 0.154 0.007 22.670 0.000 #> y3 0.164 0.008 20.711 0.000 #> X 0.983 0.036 26.994 0.000 #> Z 1.019 0.038 26.951 0.000 #> Y 0.943 0.038 24.820 0.000"},{"path":"/articles/modsem.html","id":"more-complicated-examples","dir":"Articles","previous_headings":"The Basic Syntax","what":"More Complicated Examples","title":"modsem","text":"can see complicated example using model theory planned behaviour. example included two quadratic- one interaction effect, using included dataset jordan. dataset subset PISA 2006 dataset. Note: approaches work well, might quite slow depending number interaction effects (particularly LMS- constrained approach).","code":"tpb <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) INT ~ ATT + SN + PBC BEH ~ INT + PBC + INT:PBC ' # the double centering apporach est_tpb <- modsem(tpb, TPB) # using the lms approach est_tpb_lms <- modsem(tpb, TPB, method = \"lms\") #> Warning: It is recommended that you have at least 32 nodes for interaction #> effects between exogenous and endogenous variables in the lms approach 'nodes = #> 24' summary(est_tpb_lms) #> Estimating null model #> EM: Iteration = 1, LogLik = -26393.22, Change = -26393.223 #> EM: Iteration = 2, LogLik = -26393.22, Change = 0.000 #> #> modsem (version 1.0.3): #> Estimator LMS #> Optimization method EM-NLMINB #> Number of observations 2000 #> Number of iterations 103 #> Loglikelihood -23463.37 #> Akaike (AIC) 47034.74 #> Bayesian (BIC) 47337.19 #> #> Numerical Integration: #> Points of integration (per dim) 24 #> Dimensions 1 #> Total points of integration 24 #> #> Fit Measures for H0: #> Loglikelihood -26393 #> Akaike (AIC) 52892.45 #> Bayesian (BIC) 53189.29 #> Chi-square 66.27 #> Degrees of Freedom (Chi-square) 82 #> P-value (Chi-square) 0.897 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 2929.85 #> Difference test (D) 5859.70 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> INT 0.361 #> BEH 0.248 #> R-Squared Null-Model (H0): #> INT 0.367 #> BEH 0.210 #> R-Squared Change: #> INT -0.006 #> BEH 0.038 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information expected #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> PBC =~ #> pbc1 1.000 #> pbc2 0.911 0.013 67.91 0.000 #> pbc3 0.802 0.012 65.67 0.000 #> ATT =~ #> att1 1.000 #> att2 0.877 0.012 71.32 0.000 #> att3 0.789 0.012 65.69 0.000 #> att4 0.695 0.011 60.84 0.000 #> att5 0.887 0.013 70.49 0.000 #> SN =~ #> sn1 1.000 #> sn2 0.889 0.017 51.79 0.000 #> INT =~ #> int1 1.000 #> int2 0.913 0.015 59.42 0.000 #> int3 0.807 0.014 55.75 0.000 #> BEH =~ #> b1 1.000 #> b2 0.961 0.030 31.82 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> INT ~ #> PBC 0.217 0.030 7.29 0.000 #> ATT 0.213 0.026 8.28 0.000 #> SN 0.177 0.028 6.34 0.000 #> BEH ~ #> PBC 0.228 0.023 10.06 0.000 #> INT 0.182 0.025 7.37 0.000 #> PBC:INT 0.204 0.019 10.98 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> pbc1 0.959 0.019 50.31 0.000 #> pbc2 0.950 0.018 53.08 0.000 #> pbc3 0.960 0.016 59.11 0.000 #> att1 0.987 0.022 44.10 0.000 #> att2 0.983 0.020 49.45 0.000 #> att3 0.995 0.018 54.27 0.000 #> att4 0.980 0.017 58.41 0.000 #> att5 0.969 0.020 48.14 0.000 #> sn1 0.979 0.023 43.04 0.000 #> sn2 0.987 0.020 48.23 0.000 #> int1 0.995 0.022 46.17 0.000 #> int2 0.995 0.020 49.49 0.000 #> int3 0.990 0.018 53.60 0.000 #> b1 0.989 0.022 45.86 0.000 #> b2 1.008 0.020 50.01 0.000 #> INT 0.000 #> BEH 0.000 #> PBC 0.000 #> ATT 0.000 #> SN 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> PBC ~~ #> ATT 0.658 0.020 32.31 0.000 #> SN 0.657 0.021 30.92 0.000 #> ATT ~~ #> SN 0.616 0.019 32.92 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> pbc1 0.147 0.008 19.39 0.000 #> pbc2 0.164 0.007 22.22 0.000 #> pbc3 0.154 0.006 24.15 0.000 #> att1 0.167 0.007 23.38 0.000 #> att2 0.150 0.006 24.30 0.000 #> att3 0.159 0.006 26.67 0.000 #> att4 0.163 0.006 27.66 0.000 #> att5 0.159 0.006 24.78 0.000 #> sn1 0.178 0.015 12.12 0.000 #> sn2 0.156 0.012 13.00 0.000 #> int1 0.157 0.009 18.18 0.000 #> int2 0.160 0.008 20.21 0.000 #> int3 0.168 0.007 23.39 0.000 #> b1 0.186 0.019 10.00 0.000 #> b2 0.135 0.017 8.03 0.000 #> PBC 0.933 0.015 60.19 0.000 #> ATT 0.985 0.014 70.17 0.000 #> SN 0.974 0.015 63.87 0.000 #> INT 0.491 0.020 24.40 0.000 #> BEH 0.456 0.022 20.28 0.000 m2 <- ' ENJ =~ enjoy1 + enjoy2 + enjoy3 + enjoy4 + enjoy5 CAREER =~ career1 + career2 + career3 + career4 SC =~ academic1 + academic2 + academic3 + academic4 + academic5 + academic6 CAREER ~ ENJ + SC + ENJ:ENJ + SC:SC + ENJ:SC ' est_jordan <- modsem(m2, data = jordan) est_jordan_qml <- modsem(m2, data = jordan, method = \"qml\") summary(est_jordan_qml) #> Estimating null model #> Starting M-step #> #> modsem (version 1.0.3): #> Estimator QML #> Optimization method NLMINB #> Number of observations 6038 #> Number of iterations 101 #> Loglikelihood -110520.22 #> Akaike (AIC) 221142.45 #> Bayesian (BIC) 221484.44 #> #> Fit Measures for H0: #> Loglikelihood -110521 #> Akaike (AIC) 221138.58 #> Bayesian (BIC) 221460.46 #> Chi-square 1016.34 #> Degrees of Freedom (Chi-square) 87 #> P-value (Chi-square) 0.000 #> RMSEA 0.005 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 1.07 #> Difference test (D) 2.13 #> Degrees of freedom (D) 3 #> P-value (D) 0.546 #> #> R-Squared: #> CAREER 0.512 #> R-Squared Null-Model (H0): #> CAREER 0.510 #> R-Squared Change: #> CAREER 0.002 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information observed #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> ENJ =~ #> enjoy1 1.000 #> enjoy2 1.002 0.020 50.587 0.000 #> enjoy3 0.894 0.020 43.669 0.000 #> enjoy4 0.999 0.021 48.227 0.000 #> enjoy5 1.047 0.021 50.400 0.000 #> SC =~ #> academic1 1.000 #> academic2 1.104 0.028 38.946 0.000 #> academic3 1.235 0.030 41.720 0.000 #> academic4 1.254 0.030 41.828 0.000 #> academic5 1.113 0.029 38.647 0.000 #> academic6 1.198 0.030 40.356 0.000 #> CAREER =~ #> career1 1.000 #> career2 1.040 0.016 65.180 0.000 #> career3 0.952 0.016 57.838 0.000 #> career4 0.818 0.017 48.358 0.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> CAREER ~ #> ENJ 0.523 0.020 26.286 0.000 #> SC 0.467 0.023 19.884 0.000 #> ENJ:ENJ 0.026 0.022 1.206 0.228 #> ENJ:SC -0.039 0.046 -0.851 0.395 #> SC:SC -0.002 0.035 -0.058 0.953 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> enjoy1 0.000 0.013 -0.008 0.994 #> enjoy2 0.000 0.015 0.010 0.992 #> enjoy3 0.000 0.013 -0.023 0.982 #> enjoy4 0.000 0.014 0.008 0.993 #> enjoy5 0.000 0.014 0.025 0.980 #> academic1 0.000 0.016 -0.009 0.993 #> academic2 0.000 0.014 -0.009 0.993 #> academic3 0.000 0.015 -0.028 0.978 #> academic4 0.000 0.016 -0.015 0.988 #> academic5 -0.001 0.014 -0.044 0.965 #> academic6 0.001 0.015 0.048 0.962 #> career1 -0.004 0.017 -0.204 0.838 #> career2 -0.004 0.018 -0.248 0.804 #> career3 -0.004 0.017 -0.214 0.830 #> career4 -0.004 0.016 -0.232 0.816 #> CAREER 0.000 #> ENJ 0.000 #> SC 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> ENJ ~~ #> SC 0.218 0.009 25.477 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> enjoy1 0.487 0.011 44.335 0.000 #> enjoy2 0.488 0.011 44.406 0.000 #> enjoy3 0.596 0.012 48.233 0.000 #> enjoy4 0.488 0.011 44.561 0.000 #> enjoy5 0.442 0.010 42.470 0.000 #> academic1 0.645 0.013 49.813 0.000 #> academic2 0.566 0.012 47.864 0.000 #> academic3 0.473 0.011 44.319 0.000 #> academic4 0.455 0.010 43.579 0.000 #> academic5 0.565 0.012 47.695 0.000 #> academic6 0.502 0.011 45.434 0.000 #> career1 0.373 0.009 40.392 0.000 #> career2 0.328 0.009 37.019 0.000 #> career3 0.436 0.010 43.272 0.000 #> career4 0.576 0.012 48.372 0.000 #> ENJ 0.500 0.017 29.547 0.000 #> SC 0.338 0.015 23.195 0.000 #> CAREER 0.302 0.010 29.711 0.000"},{"path":"/articles/observed_lms_qml.html","id":"the-latent-moderated-structural-equations-lms-and-the-quasi-maximum-likelihood-qml-approach","dir":"Articles","previous_headings":"","what":"The Latent Moderated Structural Equations (LMS) and the Quasi Maximum Likelihood (QML) approach","title":"observed variables in the LMS- and QML approach","text":"contrast approaches, LMS QML approaches designed handle latent variables . Thus observed variables easily used, approaches. One way getting around specifying observed variable latent variable single indicator. modsem() default constrain factor loading 1, residual variance indicator 0. , difference latent variable indicator, (assuming exogenous variable) zero-mean. work LMS- QML approach cases, except two exceptions.","code":""},{"path":"/articles/observed_lms_qml.html","id":"the-lms-approach","dir":"Articles","previous_headings":"The Latent Moderated Structural Equations (LMS) and the Quasi Maximum Likelihood (QML) approach","what":"The LMS approach","title":"observed variables in the LMS- and QML approach","text":"LMS approach can use mentioned approach almost cases, except case wish use observed variable moderating variable. LMS approach, usually select one variable interaction term moderator. interaction effect estimated via numerical integration, n quadrature nodes moderating variable. process however, requires moderating variable error-term, distribution moderating variable modelled X∼N(Az,ε)X \\sim N(Az, \\varepsilon), AzAz expected value XX quadrature point k, ε\\varepsilon error term. error-term zero, probability observing given value XX computable. instances first variable interaction term, chosen moderator. example, interaction term \"X:Z\", \"X\" usually chosen moderator. Thus one variables latent, put latent variable first interaction term. observed, specify measurement error (e.g., “x1 ~~ 0.1 * x1”) indicator first variable interaction term.","code":"library(modsem) # interaction effect between a latent and an observed variable m1 <- ' # Outer Model X =~ x1 # X is observed Z =~ z1 + z2 # Z is latent Y =~ y1 # Y is observed # Inner model Y ~ X + Z Y ~ Z:X ' lms1 <- modsem(m1, oneInt, method = \"lms\") # interaction effect between two observed variables m2 <- ' # Outer Model X =~ x1 # X is observed Z =~ z1 # Z is observed Y =~ y1 # Y is observed x1 ~~ 0.1 * x1 # specify a variance for the measurement error # Inner model Y ~ X + Z Y ~ X:Z ' lms2 <- modsem(m1, oneInt, method = \"lms\") summary(lms2) #> Estimating null model #> EM: Iteration = 1, LogLik = -10816.13, Change = -10816.126 #> EM: Iteration = 2, LogLik = -10816.13, Change = 0.000 #> #> modsem (version 1.0.3): #> Estimator LMS #> Optimization method EM-NLMINB #> Number of observations 2000 #> Number of iterations 58 #> Loglikelihood -8087.2 #> Akaike (AIC) 16202.4 #> Bayesian (BIC) 16280.81 #> #> Numerical Integration: #> Points of integration (per dim) 24 #> Dimensions 1 #> Total points of integration 24 #> #> Fit Measures for H0: #> Loglikelihood -10816 #> Akaike (AIC) 21658.25 #> Bayesian (BIC) 21731.06 #> Chi-square 0.01 #> Degrees of Freedom (Chi-square) 1 #> P-value (Chi-square) 0.917 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 2728.93 #> Difference test (D) 5457.85 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> Y 0.510 #> R-Squared Null-Model (H0): #> Y 0.343 #> R-Squared Change: #> Y 0.167 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information expected #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> Z =~ #> z1 1.000 #> z2 0.811 0.016 50.04 0.000 #> X =~ #> x1 1.000 #> Y =~ #> y1 1.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> Y ~ #> Z 0.587 0.033 17.65 0.000 #> X 0.574 0.030 19.03 0.000 #> Z:X 0.627 0.026 24.18 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> z1 1.009 0.027 37.84 0.000 #> z2 1.203 0.022 54.45 0.000 #> x1 1.023 0.027 38.49 0.000 #> y1 1.046 0.037 28.54 0.000 #> Y 0.000 #> Z 0.000 #> X 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> Z ~~ #> X 0.211 0.028 7.66 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> z1 0.170 0.017 10.24 0.000 #> z2 0.160 0.011 13.94 0.000 #> x1 0.000 #> y1 0.000 #> Z 1.010 0.020 51.26 0.000 #> X 1.141 0.017 69.00 0.000 #> Y 1.284 0.043 30.19 0.000"},{"path":"/articles/observed_lms_qml.html","id":"the-qml-approach","dir":"Articles","previous_headings":"The Latent Moderated Structural Equations (LMS) and the Quasi Maximum Likelihood (QML) approach","what":"The QML approach","title":"observed variables in the LMS- and QML approach","text":"estimation QML approach different LMS approach, issue LMS approach. Thus don’t specify measurement error moderating variables.","code":"m3 <- ' # Outer Model X =~ x1 # X is observed Z =~ z1 # Z is observed Y =~ y1 # Y is observed # Inner model Y ~ X + Z Y ~ X:Z ' qml3 <- modsem(m3, oneInt, method = \"qml\") summary(qml3) #> Estimating null model #> Starting M-step #> #> modsem (version 1.0.3): #> Estimator QML #> Optimization method NLMINB #> Number of observations 2000 #> Number of iterations 11 #> Loglikelihood -9117.07 #> Akaike (AIC) 18254.13 #> Bayesian (BIC) 18310.14 #> #> Fit Measures for H0: #> Loglikelihood -9369 #> Akaike (AIC) 18756.46 #> Bayesian (BIC) 18806.87 #> Chi-square 0.00 #> Degrees of Freedom (Chi-square) 0 #> P-value (Chi-square) 0.000 #> RMSEA 0.000 #> #> Comparative fit to H0 (no interaction effect) #> Loglikelihood change 252.17 #> Difference test (D) 504.33 #> Degrees of freedom (D) 1 #> P-value (D) 0.000 #> #> R-Squared: #> Y 0.470 #> R-Squared Null-Model (H0): #> Y 0.320 #> R-Squared Change: #> Y 0.150 #> #> Parameter Estimates: #> Coefficients unstandardized #> Information observed #> Standard errors standard #> #> Latent Variables: #> Estimate Std.Error z.value P(>|z|) #> X =~ #> x1 1.000 #> Z =~ #> z1 1.000 #> Y =~ #> y1 1.000 #> #> Regressions: #> Estimate Std.Error z.value P(>|z|) #> Y ~ #> X 0.605 0.028 21.26 0.000 #> Z 0.490 0.028 17.55 0.000 #> X:Z 0.544 0.023 23.95 0.000 #> #> Intercepts: #> Estimate Std.Error z.value P(>|z|) #> x1 1.023 0.024 42.83 0.000 #> z1 1.011 0.024 41.56 0.000 #> y1 1.066 0.034 31.64 0.000 #> Y 0.000 #> X 0.000 #> Z 0.000 #> #> Covariances: #> Estimate Std.Error z.value P(>|z|) #> X ~~ #> Z 0.210 0.026 7.95 0.000 #> #> Variances: #> Estimate Std.Error z.value P(>|z|) #> x1 0.000 #> z1 0.000 #> y1 0.000 #> X 1.141 0.036 31.62 0.000 #> Z 1.184 0.037 31.62 0.000 #> Y 1.399 0.044 31.62 0.000"},{"path":"/articles/plot_interactions.html","id":"plotting-interaction-effects","dir":"Articles","previous_headings":"","what":"Plotting interaction effects","title":"plotting interaction effects","text":"Interaction effects can plotted using included plot_interaction function. function takes fitted model object names two variables interacting. function plot interaction effect two variables. x-variable plotted x-axis y-variable plotted y-axis. z-variable decides points z effect x y plotted. function also plot 95% confidence interval interaction effect. can see simple example using double centering approach. can see different example using LMS approach, theory planned behavior model.","code":"m1 <- \" # Outer Model X =~ x1 X =~ x2 + x3 Z =~ z1 + z2 + z3 Y =~ y1 + y2 + y3 # Inner model Y ~ X + Z + X:Z \" est1 <- modsem(m1, data = oneInt) plot_interaction(\"X\", \"Z\", \"Y\", \"X:Z\", -3:3, c(-0.2, 0), est1) tpb <- \" # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ PBC:INT \" est2 <- modsem(tpb, TPB, method = \"lms\") #> Warning: It is recommended that you have at least 32 nodes for interaction #> effects between exogenous and endogenous variables in the lms approach 'nodes = #> 24' plot_interaction(x = \"INT\", z = \"PBC\", y = \"BEH\", xz = \"PBC:INT\", vals_z = c(-0.5, 0.5), model = est2)"},{"path":"/authors.html","id":null,"dir":"","previous_headings":"","what":"Authors","title":"Authors and Citation","text":"Kjell Solem Slupphaug. Author, maintainer.","code":""},{"path":"/authors.html","id":"citation","dir":"","previous_headings":"","what":"Citation","title":"Authors and Citation","text":"Slupphaug, K. S., Mehmetoglu, M., & Mittner, M. (2024). modsem: R package estimating latent interactions quadratic effects. Structural Equation Modeling: Multidisciplinary Journal doi:10.1080/10705511.2024.2417409","code":"@Article{, title = {modsem: An R package for estimating latent interactions and quadratic effects}, author = {Kjell Solem Slupphaug and Mehmet Mehmetoglu and Matthias Mittner}, journal = {Structural Equation Modeling: A Multidisciplinary Journal}, year = {2024}, doi = {10.1080/10705511.2024.2417409}, }"},{"path":"/index.html","id":"modsem-","dir":"","previous_headings":"","what":"Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)","title":"Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)","text":"package allows perform interactions latent variables (.e., moderation) CB-SEM. See https://www.modsem.org tutorial.","code":""},{"path":"/index.html","id":"to-install","dir":"","previous_headings":"","what":"To Install","title":"Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)","text":"","code":"# From CRAN install.packages(\"modsem\") # Latest version from Github install.packages(\"devtools\") devtools::install_github(\"kss2k/modsem\", build_vignettes = TRUE)"},{"path":"/index.html","id":"methodsapproaches","dir":"","previous_headings":"","what":"Methods/Approaches","title":"Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)","text":"number approaches estimating interaction effects SEM. modsem(), method = \"method\" argument allows choose use. Note constraints can become quite complicated complex models, particularly interaction including enodgenous variables. method can therefore quite slow. \"uca\" = unconstrained approach (Marsh, 2004) \"rca\" = residual centering approach (Little et al., 2006) default \"pind\" = basic product indicator approach (recommended) \"lms\" = Latent Moderated Structural equations (LMS) approach, see vignette \"qml\" = Quasi Maximum Likelihood (QML) approach, see vignette estimates model Mplus, installed","code":""},{"path":[]},{"path":"/index.html","id":"one-interaction","dir":"","previous_headings":"","what":"One interaction","title":"Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)","text":"","code":"library(modsem) m1 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' # Double centering approach est1_dca <- modsem(m1, oneInt) summary(est1_dca) # Constrained approach est1_ca <- modsem(m1, oneInt, method = \"ca\") summary(est1_ca) # QML approach est1_qml <- modsem(m1, oneInt, method = \"qml\") summary(est1_qml, standardized = TRUE) # LMS approach est1_lms <- modsem(m1, oneInt, method = \"lms\") summary(est1_lms)"},{"path":"/index.html","id":"theory-of-planned-behavior","dir":"","previous_headings":"","what":"Theory Of Planned Behavior","title":"Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)","text":"","code":"tpb <- \" # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) # Causal Relationsships INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ PBC:INT \" # double centering approach est_tpb_dca <- modsem(tpb, data = TPB, method = \"dblcent\") summary(est_tpb_dca) # Constrained approach using Wrigths path tracing rules for generating # the appropriate constraints est_tpb_ca <- modsem(tpb, data = TPB, method = \"ca\") summary(est_tpb_ca) # LMS approach est_tpb_lms <- modsem(tpb, data = TPB, method = \"lms\") summary(est_tpb_lms, standardized = TRUE) # QML approach est_tpb_qml <- modsem(tpb, data = TPB, method = \"qml\") summary(est_tpb_qml, standardized = TRUE)"},{"path":"/index.html","id":"interactions-between-two-observed-variables","dir":"","previous_headings":"","what":"Interactions between two observed variables","title":"Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)","text":"","code":"est2 <- modsem('y1 ~ x1 + z1 + x1:z1', data = oneInt, method = \"pind\") summary(est2) ## Interaction between an obsereved and a latent variable m3 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 # Inner model Y ~ X + z1 + X:z1 ' est3 <- modsem(m3, oneInt, method = \"pind\") summary(est3)"},{"path":"/reference/TPB.html","id":null,"dir":"Reference","previous_headings":"","what":"TPB — TPB","title":"TPB — TPB","text":"simulated dataset based Theory Planned Behaviour","code":""},{"path":"/reference/TPB.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"TPB — TPB","text":"","code":"tpb <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) INT ~ ATT + SN + PBC BEH ~ INT + PBC + INT:PBC ' est <- modsem(tpb, data = TPB)"},{"path":"/reference/TPB_UK.html","id":null,"dir":"Reference","previous_headings":"","what":"TPB_UK — TPB_UK","title":"TPB_UK — TPB_UK","text":"dataset based Theory Planned Behaviour UK sample. 4 variables high communality selected latent variable (ATT, SN, PBC, INT, BEH), two time points (t1 t2).","code":""},{"path":"/reference/TPB_UK.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"TPB_UK — TPB_UK","text":"Gathered replciation study original Hagger et al. (2023). Obtained https://doi.org/10.23668/psycharchives.12187","code":""},{"path":"/reference/TPB_UK.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"TPB_UK — TPB_UK","text":"","code":"tpb_uk <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att3 + att2 + att1 + att4 SN =~ sn4 + sn2 + sn3 + sn1 PBC =~ pbc2 + pbc1 + pbc3 + pbc4 INT =~ int2 + int1 + int3 + int4 BEH =~ beh3 + beh2 + beh1 + beh4 # Inner Model (Based on Steinmetz et al., 2011) # Causal Relationsships INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ INT:PBC ' est <- modsem(tpb_uk, data = TPB_UK)"},{"path":"/reference/coef_modsem_da.html","id":null,"dir":"Reference","previous_headings":"","what":"Wrapper for coef — coef_modsem_da","title":"Wrapper for coef — coef_modsem_da","text":"wrapper coef, used modsem::coef_modsem_da, since coef namespace modsem, stats","code":""},{"path":"/reference/coef_modsem_da.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Wrapper for coef — coef_modsem_da","text":"","code":"coef_modsem_da(object, ...)"},{"path":"/reference/coef_modsem_da.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Wrapper for coef — coef_modsem_da","text":"object fittet model inspect ... additional arguments","code":""},{"path":"/reference/compare_fit.html","id":null,"dir":"Reference","previous_headings":"","what":"compare model fit for qml and lms models — compare_fit","title":"compare model fit for qml and lms models — compare_fit","text":"Compare fit two models using likelihood ratio test. `estH0` representing null hypothesis model, `estH1` alternative hypothesis model. Importantly, function assumes `estH0` free parameters (.e., degrees freedom) `estH1`. alternative hypothesis model","code":""},{"path":"/reference/compare_fit.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"compare model fit for qml and lms models — compare_fit","text":"","code":"compare_fit(estH0, estH1)"},{"path":"/reference/compare_fit.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"compare model fit for qml and lms models — compare_fit","text":"estH0 object class `modsem_da` representing null hypothesis model estH1 object class `modsem_da` representing ","code":""},{"path":"/reference/compare_fit.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"compare model fit for qml and lms models — compare_fit","text":"","code":"if (FALSE) { # \\dontrun{ H0 <- \" # Outer Model X =~ x1 + x2 + x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z \" estH0 <- modsem(m1, oneInt, \"lms\") H1 <- \" # Outer Model X =~ x1 + x2 + x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z \" estH1 <- modsem(m1, oneInt, \"lms\") compare_fit(estH0, estH1) } # }"},{"path":"/reference/default_settings_da.html","id":null,"dir":"Reference","previous_headings":"","what":"default arguments fro LMS and QML approach — default_settings_da","title":"default arguments fro LMS and QML approach — default_settings_da","text":"function returns default settings LMS QML approach.","code":""},{"path":"/reference/default_settings_da.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"default arguments fro LMS and QML approach — default_settings_da","text":"","code":"default_settings_da(method = c(\"lms\", \"qml\"))"},{"path":"/reference/default_settings_da.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"default arguments fro LMS and QML approach — default_settings_da","text":"method method get settings ","code":""},{"path":"/reference/default_settings_da.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"default arguments fro LMS and QML approach — default_settings_da","text":"list","code":""},{"path":"/reference/default_settings_da.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"default arguments fro LMS and QML approach — default_settings_da","text":"","code":"library(modsem) default_settings_da() #> $lms #> $lms$verbose #> [1] FALSE #> #> $lms$optimize #> [1] TRUE #> #> $lms$nodes #> [1] 24 #> #> $lms$convergence #> [1] 1e-04 #> #> $lms$optimizer #> [1] \"nlminb\" #> #> $lms$center.data #> [1] FALSE #> #> $lms$standardize.data #> [1] FALSE #> #> $lms$standardize.out #> [1] FALSE #> #> $lms$standardize #> [1] FALSE #> #> $lms$mean.observed #> [1] TRUE #> #> $lms$double #> [1] FALSE #> #> $lms$calc.se #> [1] TRUE #> #> $lms$FIM #> [1] \"expected\" #> #> $lms$OFIM.hessian #> [1] FALSE #> #> $lms$EFIM.S #> [1] 30000 #> #> $lms$EFIM.parametric #> [1] TRUE #> #> $lms$robust.se #> [1] FALSE #> #> $lms$max.iter #> [1] 500 #> #> $lms$max.step #> [1] 1 #> #> $lms$fix.estep #> [1] TRUE #> #> $lms$epsilon #> [1] 1e-04 #> #> $lms$quad.range #> [1] Inf #> #> $lms$n.threads #> NULL #> #> #> $qml #> $qml$verbose #> [1] FALSE #> #> $qml$optimize #> [1] TRUE #> #> $qml$nodes #> [1] 0 #> #> $qml$convergence #> [1] 1e-06 #> #> $qml$optimizer #> [1] \"nlminb\" #> #> $qml$center.data #> [1] FALSE #> #> $qml$standardize #> [1] FALSE #> #> $qml$standardize.data #> [1] FALSE #> #> $qml$standardize.out #> [1] FALSE #> #> $qml$mean.observed #> [1] TRUE #> #> $qml$double #> [1] FALSE #> #> $qml$calc.se #> [1] TRUE #> #> $qml$FIM #> [1] \"observed\" #> #> $qml$OFIM.hessian #> [1] TRUE #> #> $qml$EFIM.S #> [1] 30000 #> #> $qml$EFIM.parametric #> [1] TRUE #> #> $qml$robust.se #> [1] FALSE #> #> $qml$max.iter #> [1] 500 #> #> $qml$max.step #> NULL #> #> $qml$fix.estep #> NULL #> #> $qml$epsilon #> [1] 1e-08 #> #> $qml$quad.range #> [1] Inf #> #> $qml$n.threads #> NULL #> #>"},{"path":"/reference/default_settings_pi.html","id":null,"dir":"Reference","previous_headings":"","what":"default arguments for product indicator approaches — default_settings_pi","title":"default arguments for product indicator approaches — default_settings_pi","text":"function returns default settings product indicator approaches","code":""},{"path":"/reference/default_settings_pi.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"default arguments for product indicator approaches — default_settings_pi","text":"","code":"default_settings_pi(method = c(\"rca\", \"uca\", \"pind\", \"dblcent\", \"ca\"))"},{"path":"/reference/default_settings_pi.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"default arguments for product indicator approaches — default_settings_pi","text":"method method get settings ","code":""},{"path":"/reference/default_settings_pi.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"default arguments for product indicator approaches — default_settings_pi","text":"list","code":""},{"path":"/reference/default_settings_pi.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"default arguments for product indicator approaches — default_settings_pi","text":"","code":"library(modsem) default_settings_pi() #> $rca #> $rca$center.before #> [1] FALSE #> #> $rca$center.after #> [1] FALSE #> #> $rca$residuals.prods #> [1] TRUE #> #> $rca$residual.cov.syntax #> [1] TRUE #> #> $rca$constrained.prod.mean #> [1] FALSE #> #> $rca$constrained.loadings #> [1] FALSE #> #> $rca$constrained.var #> [1] FALSE #> #> $rca$constrained.res.cov.method #> [1] \"simple\" #> #> $rca$match #> [1] FALSE #> #> #> $uca #> $uca$center.before #> [1] TRUE #> #> $uca$center.after #> [1] FALSE #> #> $uca$residuals.prods #> [1] FALSE #> #> $uca$residual.cov.syntax #> [1] TRUE #> #> $uca$constrained.prod.mean #> [1] TRUE #> #> $uca$constrained.loadings #> [1] FALSE #> #> $uca$constrained.var #> [1] FALSE #> #> $uca$constrained.res.cov.method #> [1] \"simple\" #> #> $uca$match #> [1] FALSE #> #> #> $pind #> $pind$center.before #> [1] FALSE #> #> $pind$center.after #> [1] FALSE #> #> $pind$residuals.prods #> [1] FALSE #> #> $pind$residual.cov.syntax #> [1] FALSE #> #> $pind$constrained.prod.mean #> [1] FALSE #> #> $pind$constrained.loadings #> [1] FALSE #> #> $pind$constrained.var #> [1] FALSE #> #> $pind$constrained.res.cov.method #> [1] \"simple\" #> #> $pind$match #> [1] FALSE #> #> #> $dblcent #> $dblcent$center.before #> [1] TRUE #> #> $dblcent$center.after #> [1] TRUE #> #> $dblcent$residuals.prods #> [1] FALSE #> #> $dblcent$residual.cov.syntax #> [1] TRUE #> #> $dblcent$constrained.prod.mean #> [1] FALSE #> #> $dblcent$constrained.loadings #> [1] FALSE #> #> $dblcent$constrained.var #> [1] FALSE #> #> $dblcent$constrained.res.cov.method #> [1] \"simple\" #> #> $dblcent$match #> [1] FALSE #> #> #> $ca #> $ca$center.before #> [1] TRUE #> #> $ca$center.after #> [1] FALSE #> #> $ca$residuals.prods #> [1] FALSE #> #> $ca$residual.cov.syntax #> [1] TRUE #> #> $ca$constrained.prod.mean #> [1] TRUE #> #> $ca$constrained.loadings #> [1] TRUE #> #> $ca$constrained.var #> [1] TRUE #> #> $ca$constrained.res.cov.method #> [1] \"ca\" #> #> $ca$match #> [1] TRUE #> #>"},{"path":"/reference/extract_lavaan.html","id":null,"dir":"Reference","previous_headings":"","what":"extract lavaan object from modsem object estimated using product indicators — extract_lavaan","title":"extract lavaan object from modsem object estimated using product indicators — extract_lavaan","text":"extract lavaan object modsem object estimated using product indicators","code":""},{"path":"/reference/extract_lavaan.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"extract lavaan object from modsem object estimated using product indicators — extract_lavaan","text":"","code":"extract_lavaan(object)"},{"path":"/reference/extract_lavaan.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"extract lavaan object from modsem object estimated using product indicators — extract_lavaan","text":"object modsem object","code":""},{"path":"/reference/extract_lavaan.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"extract lavaan object from modsem object estimated using product indicators — extract_lavaan","text":"lavaan object","code":""},{"path":"/reference/extract_lavaan.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"extract lavaan object from modsem object estimated using product indicators — extract_lavaan","text":"","code":"library(modsem) m1 <- ' # Outer Model X =~ x1 + x2 + x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' est <- modsem_pi(m1, oneInt) lav_est <- extract_lavaan(est)"},{"path":"/reference/fit_modsem_da.html","id":null,"dir":"Reference","previous_headings":"","what":"Fit measures for QML and LMS models — fit_modsem_da","title":"Fit measures for QML and LMS models — fit_modsem_da","text":"Calculates chi-sq test p-value, well RMSEA LMS QML models. Note Chi-Square based fit measures calculated baseline model, .e., model without interaction effect","code":""},{"path":"/reference/fit_modsem_da.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Fit measures for QML and LMS models — fit_modsem_da","text":"","code":"fit_modsem_da(model, chisq = TRUE)"},{"path":"/reference/fit_modsem_da.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Fit measures for QML and LMS models — fit_modsem_da","text":"model fitted model. Thereafter, can use 'compare_fit()' assess comparative fit models. interaction effect makes model better, e.g., RMSEA good baseline model, interaction model likely good RMSEA well. chisq Chi-Square based fit-measures calculated?","code":""},{"path":"/reference/get_pi_data.html","id":null,"dir":"Reference","previous_headings":"","what":"Get data with product indicators for different approaches — get_pi_data","title":"Get data with product indicators for different approaches — get_pi_data","text":"get_pi_syntax() function creating lavaan syntax used estimating latent interaction models using one product indicators lavaan.","code":""},{"path":"/reference/get_pi_data.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get data with product indicators for different approaches — get_pi_data","text":"","code":"get_pi_data(model.syntax, data, method = \"dblcent\", match = FALSE, ...)"},{"path":"/reference/get_pi_data.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get data with product indicators for different approaches — get_pi_data","text":"model.syntax lavaan syntax data data create product indicators method method use: \"rca\" = residual centering approach, \"uca\" = unconstrained approach, \"dblcent\" = double centering approach, \"pind\" = prod ind approach, constraints centering, \"custom\" = use parameters specified function call match product indicators created using match-strategy ... arguments passed functions (e.g., modsem_pi)","code":""},{"path":"/reference/get_pi_data.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get data with product indicators for different approaches — get_pi_data","text":"data.frame","code":""},{"path":"/reference/get_pi_data.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Get data with product indicators for different approaches — get_pi_data","text":"","code":"library(modsem) library(lavaan) #> This is lavaan 0.6-19 #> lavaan is FREE software! Please report any bugs. m1 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' syntax <- get_pi_syntax(m1) data <- get_pi_data(m1, oneInt) est <- sem(syntax, data)"},{"path":"/reference/get_pi_syntax.html","id":null,"dir":"Reference","previous_headings":"","what":"Get lavaan syntax for product indicator approaches — get_pi_syntax","title":"Get lavaan syntax for product indicator approaches — get_pi_syntax","text":"get_pi_syntax() function creating lavaan syntax used estimating latent interaction models using one product indicators lavaan.","code":""},{"path":"/reference/get_pi_syntax.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get lavaan syntax for product indicator approaches — get_pi_syntax","text":"","code":"get_pi_syntax(model.syntax, method = \"dblcent\", match = FALSE, ...)"},{"path":"/reference/get_pi_syntax.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get lavaan syntax for product indicator approaches — get_pi_syntax","text":"model.syntax lavaan syntax method method use: \"rca\" = residual centering approach, \"uca\" = unconstrained approach, \"dblcent\" = double centering approach, \"pind\" = prod ind approach, constraints centering, \"custom\" = use parameters specified function call match product indicators created using match-strategy ... arguments passed functions (e.g., modsem_pi)","code":""},{"path":"/reference/get_pi_syntax.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Get lavaan syntax for product indicator approaches — get_pi_syntax","text":"character vector","code":""},{"path":"/reference/get_pi_syntax.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Get lavaan syntax for product indicator approaches — get_pi_syntax","text":"","code":"library(modsem) library(lavaan) m1 <- ' # Outer Model X =~ x1 + x2 + x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' syntax <- get_pi_syntax(m1) data <- get_pi_data(m1, oneInt) est <- sem(syntax, data)"},{"path":"/reference/jordan.html","id":null,"dir":"Reference","previous_headings":"","what":"Jordan subset of PISA 2006 data — jordan","title":"Jordan subset of PISA 2006 data — jordan","text":"data stem large-scale assessment study PISA 2006 (Organisation Economic Co-Operation Development, 2009) competencies 15-year-old students reading, mathematics, science assessed using nationally representative samples 3-year cycles. eacademicample, data student background questionnaire Jordan sample PISA 2006 used. data students complete responses 15 items (N = 6,038) considered.","code":""},{"path":"/reference/jordan.html","id":"format","dir":"Reference","previous_headings":"","what":"Format","title":"Jordan subset of PISA 2006 data — jordan","text":"data frame fifteen variables 6,038 observations: enjoy1 indicator enjoyment science, item ST16Q01: generally fun learning topics. enjoy2 indicator enjoyment science, item ST16Q02: like reading . enjoy3 indicator enjoyment science, item ST16Q03: happy problems. enjoy4 indicator enjoyment science, item ST16Q04: enjoy acquiring new knowledge . enjoy5 indicator enjoyment science, item ST16Q05: interested learning . academic1 indicator academic self-concept science, item ST37Q01: can easily understand new ideas . academic2 indicator academic self-concept science, item ST37Q02: Learning advanced topics easy . academic3 indicator academic self-concept science, item ST37Q03: can usually give good answers topics. academic4 indicator academic self-concept science, item ST37Q04: learn topics quickly. academic5 indicator academic self-concept science, item ST37Q05: topics easy . academic6 indicator academic self-concept science, item ST37Q06: taught , can understand concepts well. career1 indicator career aspirations science, item ST29Q01: like work career involving . career2 indicator career aspirations science, item ST29Q02: like study . career3 indicator career aspirations science, item ST29Q03: like spend life advanced . career4 indicator career aspirations science, item ST29Q04: like work projects adult.","code":""},{"path":"/reference/jordan.html","id":"source","dir":"Reference","previous_headings":"","what":"Source","title":"Jordan subset of PISA 2006 data — jordan","text":"version dataset, well description gathered documentation 'nlsem' package (https://cran.r-project.org/package=nlsem), difference names variables changed Originally dataset gathered Organisation Economic Co-Operation Development (2009). Pisa 2006: Science competencies tomorrow's world (Tech. Rep.). Paris, France. Obtained : https://www.oecd.org/pisa/pisaproducts/database-pisa2006.htm","code":""},{"path":"/reference/jordan.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Jordan subset of PISA 2006 data — jordan","text":"","code":"if (FALSE) { # \\dontrun{ m1 <- ' ENJ =~ enjoy1 + enjoy2 + enjoy3 + enjoy4 + enjoy5 CAREER =~ career1 + career2 + career3 + career4 SC =~ academic1 + academic2 + academic3 + academic4 + academic5 + academic6 CAREER ~ ENJ + SC + ENJ:ENJ + SC:SC + ENJ:SC ' est <- modsem(m1, data = jordan) } # }"},{"path":"/reference/modsem-package.html","id":null,"dir":"Reference","previous_headings":"","what":"modsem: Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM) — modsem-package","title":"modsem: Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM) — modsem-package","text":"Estimation interaction (.e., moderation) effects latent variables structural equation models (SEM). supported methods : constrained approach (Algina & Moulder, 2001). unconstrained approach (Marsh et al., 2004). residual centering approach (Little et al., 2006). double centering approach (Lin et al., 2010). latent moderated structural equations (LMS) approach (Klein & Moosbrugger, 2000). quasi-maximum likelihood (QML) approach (Klein & Muthén, 2007) (temporarily unavailable) constrained- unconstrained, residual- double centering- approaches estimated via 'lavaan' (Rosseel, 2012), whilst LMS- QML- approaches estimated via modsem self. Alternatively model can estimated via 'Mplus' (Muthén & Muthén, 1998-2017). References: Algina, J., & Moulder, B. C. (2001). doi:10.1207/S15328007SEM0801_3 . \"note estimating Jöreskog-Yang model latent variable interaction using 'LISREL' 8.3.\" Klein, ., & Moosbrugger, H. (2000). doi:10.1007/BF02296338 . \"Maximum likelihood estimation latent interaction effects LMS method.\" Klein, . G., & Muthén, B. O. (2007). doi:10.1080/00273170701710205 . \"Quasi-maximum likelihood estimation structural equation models multiple interaction quadratic effects.\" Lin, G. C., Wen, Z., Marsh, H. W., & Lin, H. S. (2010). doi:10.1080/10705511.2010.488999 . \"Structural equation models latent interactions: Clarification orthogonalizing double-mean-centering strategies.\" Little, T. D., Bovaird, J. ., & Widaman, K. F. (2006). doi:10.1207/s15328007sem1304_1 . \"merits orthogonalizing powered product terms: Implications modeling interactions among latent variables.\" Marsh, H. W., Wen, Z., & Hau, K. T. (2004). doi:10.1037/1082-989X.9.3.275 . \"Structural equation models latent interactions: evaluation alternative estimation strategies indicator construction.\" Muthén, L.K. Muthén, B.O. (1998-2017). \"'Mplus' User’s Guide. Eighth Edition.\" https://www.statmodel.com/. Rosseel Y (2012). doi:10.18637/jss.v048.i02 . \"'lavaan': R Package Structural Equation Modeling.\"","code":""},{"path":[]},{"path":"/reference/modsem-package.html","id":"author","dir":"Reference","previous_headings":"","what":"Author","title":"modsem: Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM) — modsem-package","text":"Maintainer: Kjell Solem Slupphaug slupphaugkjell@gmail.com (ORCID)","code":""},{"path":"/reference/modsem.html","id":null,"dir":"Reference","previous_headings":"","what":"Estimate interaction effects in structural equation models (SEMs) — modsem","title":"Estimate interaction effects in structural equation models (SEMs) — modsem","text":"modsem() function estimating interaction effects latent variables structural equation models (SEMs). Methods estimating interaction effects SEMs can basically split two frameworks: 1. Product Indicator-based approaches (\"dblcent\", \"rca\", \"uca\", \"ca\", \"pind\") 2. Distributionally based approaches (\"lms\", \"qml\"). product indicator-based approaches, modsem() essentially fancy wrapper lavaan::sem() generates necessary syntax variables estimation models latent product indicators. distributionally based approaches implemented separately estimated using lavaan::sem(), rather using custom functions (largely written C++ performance reasons). greater control, advised use one sub-functions (modsem_pi, modsem_da, modsem_mplus) directly, passing additional arguments via modsem() can lead unexpected behavior.","code":""},{"path":"/reference/modsem.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Estimate interaction effects in structural equation models (SEMs) — modsem","text":"","code":"modsem(model.syntax = NULL, data = NULL, method = \"dblcent\", ...)"},{"path":"/reference/modsem.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Estimate interaction effects in structural equation models (SEMs) — modsem","text":"model.syntax lavaan syntax data dataframe method method use: \"rca\" = residual centering approach (passed lavaan), \"uca\" = unconstrained approach (passed lavaan), \"dblcent\" = double centering approach (passed lavaan), \"pind\" = prod ind approach, constraints centering (passed lavaan), \"lms\" = latent model structural equations (passed lavaan), \"qml\" = quasi maximum likelihood estimation latent model structural equations (passed lavaan), \"custom\" = use parameters specified function call (passed lavaan). ... arguments passed functions depending method (see modsem_pi, modsem_da, modsem_mplus)","code":""},{"path":"/reference/modsem.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Estimate interaction effects in structural equation models (SEMs) — modsem","text":"modsem object class modsem_pi, modsem_da, modsem_mplus","code":""},{"path":"/reference/modsem.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Estimate interaction effects in structural equation models (SEMs) — modsem","text":"","code":"library(modsem) # For more examples, check README and/or GitHub. # One interaction m1 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' # Double centering approach est1 <- modsem(m1, oneInt) summary(est1) #> modsem: #> Method = dblcent #> lavaan 0.6-19 ended normally after 159 iterations #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 60 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 122.924 #> Degrees of freedom 111 #> P-value (Chi-square) 0.207 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Latent Variables: #> Estimate Std.Err z-value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.804 0.013 63.612 0.000 #> x3 0.916 0.014 67.144 0.000 #> Y =~ #> y1 1.000 #> y2 0.798 0.007 107.428 0.000 #> y3 0.899 0.008 112.453 0.000 #> Z =~ #> z1 1.000 #> z2 0.812 0.013 64.763 0.000 #> z3 0.882 0.013 67.014 0.000 #> XZ =~ #> x1z1 1.000 #> x2z1 0.805 0.013 60.636 0.000 #> x3z1 0.877 0.014 62.680 0.000 #> x1z2 0.793 0.013 59.343 0.000 #> x2z2 0.646 0.015 43.672 0.000 #> x3z2 0.706 0.016 44.292 0.000 #> x1z3 0.887 0.014 63.700 0.000 #> x2z3 0.716 0.016 45.645 0.000 #> x3z3 0.781 0.017 45.339 0.000 #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> Y ~ #> X 0.675 0.027 25.379 0.000 #> Z 0.561 0.026 21.606 0.000 #> XZ 0.702 0.027 26.360 0.000 #> #> Covariances: #> Estimate Std.Err z-value P(>|z|) #> .x1z1 ~~ #> .x2z2 0.000 #> .x2z3 0.000 #> .x3z2 0.000 #> .x3z3 0.000 #> .x2z1 ~~ #> .x1z2 0.000 #> .x1z2 ~~ #> .x2z3 0.000 #> .x3z1 ~~ #> .x1z2 0.000 #> .x1z2 ~~ #> .x3z3 0.000 #> .x2z1 ~~ #> .x1z3 0.000 #> .x2z2 ~~ #> .x1z3 0.000 #> .x3z1 ~~ #> .x1z3 0.000 #> .x3z2 ~~ #> .x1z3 0.000 #> .x2z1 ~~ #> .x3z2 0.000 #> .x3z3 0.000 #> .x3z1 ~~ #> .x2z2 0.000 #> .x2z2 ~~ #> .x3z3 0.000 #> .x3z1 ~~ #> .x2z3 0.000 #> .x3z2 ~~ #> .x2z3 0.000 #> .x1z1 ~~ #> .x1z2 0.115 0.008 14.802 0.000 #> .x1z3 0.114 0.008 13.947 0.000 #> .x2z1 0.125 0.008 16.095 0.000 #> .x3z1 0.140 0.009 16.135 0.000 #> .x1z2 ~~ #> .x1z3 0.103 0.007 14.675 0.000 #> .x2z2 0.128 0.006 20.850 0.000 #> .x3z2 0.146 0.007 21.243 0.000 #> .x1z3 ~~ #> .x2z3 0.116 0.007 17.818 0.000 #> .x3z3 0.135 0.007 18.335 0.000 #> .x2z1 ~~ #> .x2z2 0.135 0.006 20.905 0.000 #> .x2z3 0.145 0.007 21.145 0.000 #> .x3z1 0.114 0.007 16.058 0.000 #> .x2z2 ~~ #> .x2z3 0.117 0.006 20.419 0.000 #> .x3z2 0.116 0.006 20.586 0.000 #> .x2z3 ~~ #> .x3z3 0.109 0.006 18.059 0.000 #> .x3z1 ~~ #> .x3z2 0.138 0.007 19.331 0.000 #> .x3z3 0.158 0.008 20.269 0.000 #> .x3z2 ~~ #> .x3z3 0.131 0.007 19.958 0.000 #> X ~~ #> Z 0.201 0.024 8.271 0.000 #> XZ 0.016 0.025 0.628 0.530 #> Z ~~ #> XZ 0.062 0.025 2.449 0.014 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .x1 0.160 0.009 17.871 0.000 #> .x2 0.162 0.007 22.969 0.000 #> .x3 0.163 0.008 20.161 0.000 #> .y1 0.159 0.009 17.896 0.000 #> .y2 0.154 0.007 22.640 0.000 #> .y3 0.164 0.008 20.698 0.000 #> .z1 0.168 0.009 18.143 0.000 #> .z2 0.158 0.007 22.264 0.000 #> .z3 0.158 0.008 20.389 0.000 #> .x1z1 0.311 0.014 22.227 0.000 #> .x2z1 0.292 0.011 27.287 0.000 #> .x3z1 0.327 0.012 26.275 0.000 #> .x1z2 0.290 0.011 26.910 0.000 #> .x2z2 0.239 0.008 29.770 0.000 #> .x3z2 0.270 0.009 29.117 0.000 #> .x1z3 0.272 0.012 23.586 0.000 #> .x2z3 0.245 0.009 27.979 0.000 #> .x3z3 0.297 0.011 28.154 0.000 #> X 0.981 0.036 26.895 0.000 #> .Y 0.990 0.038 25.926 0.000 #> Z 1.016 0.038 26.856 0.000 #> XZ 1.045 0.044 24.004 0.000 #> if (FALSE) { # \\dontrun{ # The Constrained Approach est1_ca <- modsem(m1, oneInt, method = \"ca\") summary(est1_ca) # LMS approach est1_lms <- modsem(m1, oneInt, method = \"lms\") summary(est1_lms) # QML approach est1_qml <- modsem(m1, oneInt, method = \"qml\") summary(est1_qml) } # } # Theory Of Planned Behavior tpb <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ INT:PBC ' # Double centering approach est_tpb <- modsem(tpb, data = TPB) summary(est_tpb) #> modsem: #> Method = dblcent #> lavaan 0.6-19 ended normally after 171 iterations #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 78 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 207.615 #> Degrees of freedom 222 #> P-value (Chi-square) 0.747 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Latent Variables: #> Estimate Std.Err z-value P(>|z|) #> ATT =~ #> att1 1.000 #> att2 0.878 0.012 71.509 0.000 #> att3 0.789 0.012 66.368 0.000 #> att4 0.695 0.011 61.017 0.000 #> att5 0.887 0.013 70.884 0.000 #> SN =~ #> sn1 1.000 #> sn2 0.889 0.017 52.553 0.000 #> PBC =~ #> pbc1 1.000 #> pbc2 0.912 0.013 69.500 0.000 #> pbc3 0.801 0.012 65.830 0.000 #> INT =~ #> int1 1.000 #> int2 0.914 0.016 58.982 0.000 #> int3 0.808 0.015 55.547 0.000 #> BEH =~ #> b1 1.000 #> b2 0.960 0.030 31.561 0.000 #> INTPBC =~ #> int1pbc1 1.000 #> int2pbc1 0.931 0.015 63.809 0.000 #> int3pbc1 0.774 0.013 60.107 0.000 #> int1pbc2 0.893 0.013 68.173 0.000 #> int2pbc2 0.826 0.017 48.845 0.000 #> int3pbc2 0.690 0.015 45.300 0.000 #> int1pbc3 0.799 0.012 67.008 0.000 #> int2pbc3 0.738 0.015 47.809 0.000 #> int3pbc3 0.622 0.014 45.465 0.000 #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> INT ~ #> ATT 0.213 0.026 8.170 0.000 #> SN 0.177 0.028 6.416 0.000 #> PBC 0.217 0.030 7.340 0.000 #> BEH ~ #> INT 0.191 0.024 7.817 0.000 #> PBC 0.230 0.022 10.507 0.000 #> INTPBC 0.204 0.018 11.425 0.000 #> #> Covariances: #> Estimate Std.Err z-value P(>|z|) #> .int1pbc1 ~~ #> .int2pbc2 0.000 #> .int2pbc3 0.000 #> .int3pbc2 0.000 #> .int3pbc3 0.000 #> .int2pbc1 ~~ #> .int1pbc2 0.000 #> .int1pbc2 ~~ #> .int2pbc3 0.000 #> .int3pbc1 ~~ #> .int1pbc2 0.000 #> .int1pbc2 ~~ #> .int3pbc3 0.000 #> .int2pbc1 ~~ #> .int1pbc3 0.000 #> .int2pbc2 ~~ #> .int1pbc3 0.000 #> .int3pbc1 ~~ #> .int1pbc3 0.000 #> .int3pbc2 ~~ #> .int1pbc3 0.000 #> .int2pbc1 ~~ #> .int3pbc2 0.000 #> .int3pbc3 0.000 #> .int3pbc1 ~~ #> .int2pbc2 0.000 #> .int2pbc2 ~~ #> .int3pbc3 0.000 #> .int3pbc1 ~~ #> .int2pbc3 0.000 #> .int3pbc2 ~~ #> .int2pbc3 0.000 #> .int1pbc1 ~~ #> .int1pbc2 0.126 0.009 14.768 0.000 #> .int1pbc3 0.102 0.007 13.794 0.000 #> .int2pbc1 0.104 0.007 14.608 0.000 #> .int3pbc1 0.091 0.006 14.109 0.000 #> .int1pbc2 ~~ #> .int1pbc3 0.095 0.007 13.852 0.000 #> .int2pbc2 0.128 0.007 19.320 0.000 #> .int3pbc2 0.119 0.006 19.402 0.000 #> .int1pbc3 ~~ #> .int2pbc3 0.110 0.006 19.911 0.000 #> .int3pbc3 0.097 0.005 19.415 0.000 #> .int2pbc1 ~~ #> .int2pbc2 0.152 0.008 18.665 0.000 #> .int2pbc3 0.138 0.007 18.779 0.000 #> .int3pbc1 0.082 0.006 13.951 0.000 #> .int2pbc2 ~~ #> .int2pbc3 0.121 0.007 18.361 0.000 #> .int3pbc2 0.104 0.005 19.047 0.000 #> .int2pbc3 ~~ #> .int3pbc3 0.087 0.005 19.180 0.000 #> .int3pbc1 ~~ #> .int3pbc2 0.139 0.007 21.210 0.000 #> .int3pbc3 0.123 0.006 21.059 0.000 #> .int3pbc2 ~~ #> .int3pbc3 0.114 0.005 21.021 0.000 #> ATT ~~ #> SN 0.629 0.029 21.977 0.000 #> PBC 0.678 0.029 23.721 0.000 #> INTPBC 0.086 0.024 3.519 0.000 #> SN ~~ #> PBC 0.678 0.029 23.338 0.000 #> INTPBC 0.055 0.025 2.230 0.026 #> PBC ~~ #> INTPBC 0.087 0.024 3.609 0.000 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .att1 0.167 0.007 23.528 0.000 #> .att2 0.150 0.006 24.693 0.000 #> .att3 0.160 0.006 26.378 0.000 #> .att4 0.163 0.006 27.649 0.000 #> .att5 0.159 0.006 24.930 0.000 #> .sn1 0.178 0.015 12.110 0.000 #> .sn2 0.156 0.012 13.221 0.000 #> .pbc1 0.145 0.008 18.440 0.000 #> .pbc2 0.160 0.007 21.547 0.000 #> .pbc3 0.154 0.007 23.716 0.000 #> .int1 0.158 0.009 18.152 0.000 #> .int2 0.160 0.008 20.345 0.000 #> .int3 0.167 0.007 23.414 0.000 #> .b1 0.186 0.018 10.058 0.000 #> .b2 0.135 0.017 8.080 0.000 #> .int1pbc1 0.266 0.013 20.971 0.000 #> .int2pbc1 0.292 0.012 24.421 0.000 #> .int3pbc1 0.251 0.010 26.305 0.000 #> .int1pbc2 0.290 0.012 24.929 0.000 #> .int2pbc2 0.269 0.010 26.701 0.000 #> .int3pbc2 0.253 0.009 29.445 0.000 #> .int1pbc3 0.223 0.009 24.431 0.000 #> .int2pbc3 0.234 0.008 27.633 0.000 #> .int3pbc3 0.203 0.007 29.288 0.000 #> ATT 0.998 0.037 27.138 0.000 #> SN 0.987 0.039 25.394 0.000 #> PBC 0.962 0.035 27.260 0.000 #> .INT 0.490 0.020 24.638 0.000 #> .BEH 0.455 0.023 20.068 0.000 #> INTPBC 1.020 0.041 24.612 0.000 #> if (FALSE) { # \\dontrun{ # The Constrained Approach est_tpb_ca <- modsem(tpb, data = TPB, method = \"ca\") summary(est_tpb_ca) # LMS approach est_tpb_lms <- modsem(tpb, data = TPB, method = \"lms\") summary(est_tpb_lms) # QML approach est_tpb_qml <- modsem(tpb, data = TPB, method = \"qml\") summary(est_tpb_qml) } # }"},{"path":"/reference/modsem_da.html","id":null,"dir":"Reference","previous_headings":"","what":"Interaction between latent variables using lms and qml approaches — modsem_da","title":"Interaction between latent variables using lms and qml approaches — modsem_da","text":"modsem_da() function estimating interaction effects latent variables structural equation models (SEMs) using distributional analytic (DA) approaches. Methods estimating interaction effects SEMs can basically split two frameworks: 1. Product Indicator-based approaches (\"dblcent\", \"rca\", \"uca\", \"ca\", \"pind\") 2. Distributionally based approaches (\"lms\", \"qml\"). modsem_da() handles latter can estimate models using QML LMS, necessary syntax, variables estimation models latent product indicators. NOTE: Run default_settings_da see default arguments.","code":""},{"path":"/reference/modsem_da.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Interaction between latent variables using lms and qml approaches — modsem_da","text":"","code":"modsem_da( model.syntax = NULL, data = NULL, method = \"lms\", verbose = NULL, optimize = NULL, nodes = NULL, convergence = NULL, optimizer = NULL, center.data = NULL, standardize.data = NULL, standardize.out = NULL, standardize = NULL, mean.observed = NULL, cov.syntax = NULL, double = NULL, calc.se = NULL, FIM = NULL, EFIM.S = NULL, OFIM.hessian = NULL, EFIM.parametric = NULL, robust.se = NULL, max.iter = NULL, max.step = NULL, fix.estep = NULL, start = NULL, epsilon = NULL, quad.range = NULL, n.threads = NULL, ... )"},{"path":"/reference/modsem_da.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Interaction between latent variables using lms and qml approaches — modsem_da","text":"model.syntax lavaan syntax data dataframe method method use: \"lms\" = latent model structural equations (passed lavaan). \"qml\" = quasi maximum likelihood estimation latent model structural equations (passed lavaan). verbose estimation progress shown optimize starting parameters optimized nodes number quadrature nodes (points integration) used lms, increased number gives better estimates slower computation. many needed depends complexity model. simple models, somewhere 16-24 nodes enough; complex models, higher numbers may needed. models interaction effect endogenous exogenous variable, number nodes least 32, practically (e.g., ordinal/skewed data), 32 recommended. cases data non-normal, might better use qml approach instead. large numbers nodes, might want change 'quad.range' argument. convergence convergence criterion. Lower values give better estimates slower computation. optimizer optimizer use, can either \"nlminb\" \"L-BFGS-B\". LMS, \"nlminb\" recommended. QML, \"L-BFGS-B\" may faster large number iterations, slower iterations. center.data data centered fitting model standardize.data data scaled fitting model, overridden standardize standardize set TRUE. NOTE: recommended estimate model normally standardize output using standardized_estimates. standardize.output standardized (note alter relationships parameter constraints since parameters scaled unevenly, even label). alter estimation model, output. NOTE: recommended estimate model normally standardize output using standardized_estimates. standardize standardize data fitting model, remove mean structure observed variables, standardize output. Note standardize.data, mean.observed, standardize.overridden standardize standardize set TRUE. NOTE: recommended estimate model normally standardize output using standardized_estimates. mean.observed mean structure observed variables estimated? overridden standardize standardize set TRUE. NOTE: recommended unless know . cov.syntax model syntax implied covariance matrix (see vignette(\"interaction_two_etas\", \"modsem\")) double try double number dimensions integration used LMS, extremely slow similar mplus. calc.se standard errors computed? NOTE: FALSE, information matrix computed either. FIM Fisher information matrix calculated using observed expected values? Must either \"observed\" \"expected\". EFIM.S expected Fisher information matrix computed, EFIM.S selects sample size generated data. OFIM.hessian observed Fisher information computed using Hessian? FALSE, computed using gradient. EFIM.parametric data calculating expected Fisher information matrix simulated parametrically (simulated based assumptions implied parameters model), non-parametrically (stochastically sampled)? believe normality assumptions violated, EFIM.parametric = FALSE might better option. robust.se robust standard errors computed? Meant used QML, can unreliable LMS approach. max.iter maximum number iterations. max.step maximum steps M-step EM algorithm (LMS). fix.estep TRUE, E-step fixed, prior probabilities set best prior probabilities, log-likelihood decreases 30 iterations. start starting parameters. epsilon finite difference numerical derivatives. quad.range range z-scores perform numerical integration LMS using Gaussian-Hermite Quadratures. default Inf, f(t) integrated -Inf Inf, likely inefficient pointless large number nodes. Nodes outside +/- quad.range ignored. n.threads number cores use parallel processing. NULL, use <= 2 threads. integer specified, use number threads (e.g., n.threads = 4 use 4 threads). \"default\", use default number threads (2). \"max\", use available threads, \"min\" use 1 thread. ... additional arguments passed estimation function.","code":""},{"path":"/reference/modsem_da.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Interaction between latent variables using lms and qml approaches — modsem_da","text":"modsem_da object","code":""},{"path":"/reference/modsem_da.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Interaction between latent variables using lms and qml approaches — modsem_da","text":"","code":"library(modsem) # For more examples, check README and/or GitHub. # One interaction m1 <- \" # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z \" if (FALSE) { # \\dontrun{ # QML Approach est1 <- modsem_da(m1, oneInt, method = \"qml\") summary(est1) # Theory Of Planned Behavior tpb <- \" # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) # Covariances ATT ~~ SN + PBC PBC ~~ SN # Causal Relationships INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ INT:PBC \" # LMS Approach estTpb <- modsem_da(tpb, data = TPB, method = lms) summary(estTpb) } # }"},{"path":"/reference/modsem_inspect.html","id":null,"dir":"Reference","previous_headings":"","what":"Inspect model information — modsem_inspect","title":"Inspect model information — modsem_inspect","text":"function used inspect fittet object. similar `lavInspect()` argument '' decides inspect","code":""},{"path":"/reference/modsem_inspect.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Inspect model information — modsem_inspect","text":"","code":"modsem_inspect(object, what = NULL, ...)"},{"path":"/reference/modsem_inspect.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Inspect model information — modsem_inspect","text":"object fittet model inspect inspect ... Additional arguments passed functions","code":""},{"path":"/reference/modsem_inspect.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Inspect model information — modsem_inspect","text":"`modsem_da`, `modsem_lavaan` `modsem_lavaan`, just wrapper `lavInspect()` `modsem_da` “ can either \"\", \"matrices\", \"optim\", just name extract.","code":""},{"path":"/reference/modsem_mplus.html","id":null,"dir":"Reference","previous_headings":"","what":"Estimation latent interactions through mplus — modsem_mplus","title":"Estimation latent interactions through mplus — modsem_mplus","text":"Estimation latent interactions mplus","code":""},{"path":"/reference/modsem_mplus.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Estimation latent interactions through mplus — modsem_mplus","text":"","code":"modsem_mplus( model.syntax, data, estimator = \"ml\", type = \"random\", algorithm = \"integration\", process = \"8\", ... )"},{"path":"/reference/modsem_mplus.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Estimation latent interactions through mplus — modsem_mplus","text":"model.syntax lavaan/modsem syntax data dataset estimator estimator argument passed mplus type type argument passed mplus algorithm algorithm argument passed mplus process process argument passed mplus ... arguments passed functions","code":""},{"path":"/reference/modsem_mplus.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Estimation latent interactions through mplus — modsem_mplus","text":"modsem_mplus object","code":""},{"path":"/reference/modsem_mplus.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Estimation latent interactions through mplus — modsem_mplus","text":"","code":"# Theory Of Planned Behavior tpb <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) # Covariances ATT ~~ SN + PBC PBC ~~ SN # Causal Relationsships INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ INT:PBC ' if (FALSE) { # \\dontrun{ estTpbMplus <- modsem_mplus(tpb, data = TPB) summary(estTpbLMS) } # }"},{"path":"/reference/modsem_pi.html","id":null,"dir":"Reference","previous_headings":"","what":"Interaction between latent variables using product indicators — modsem_pi","title":"Interaction between latent variables using product indicators — modsem_pi","text":"modsem_pi() function estimating interaction effects latent variables, structural equation models (SEMs), using product indicators. Methods estimating interaction effects SEMs can basically split two frameworks: 1. Product Indicator based approaches (\"dblcent\", \"rca\", \"uca\", \"ca\", \"pind\"), 2. Distributionally based approaches (\"lms\", \"qml\"). modsem_pi() essentially fancy wrapper lavaan::sem() generates necessary syntax variables estimation models latent product indicators. Use default_settings_pi() get default settings different methods.","code":""},{"path":"/reference/modsem_pi.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Interaction between latent variables using product indicators — modsem_pi","text":"","code":"modsem_pi( model.syntax = NULL, data = NULL, method = \"dblcent\", match = NULL, standardize.data = FALSE, center.data = FALSE, first.loading.fixed = TRUE, center.before = NULL, center.after = NULL, residuals.prods = NULL, residual.cov.syntax = NULL, constrained.prod.mean = NULL, constrained.loadings = NULL, constrained.var = NULL, constrained.res.cov.method = NULL, auto.scale = \"none\", auto.center = \"none\", estimator = \"ML\", group = NULL, run = TRUE, suppress.warnings.lavaan = FALSE, ... )"},{"path":"/reference/modsem_pi.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Interaction between latent variables using product indicators — modsem_pi","text":"model.syntax lavaan syntax data dataframe method method use: \"rca\" = residual centering approach (passed lavaan), \"uca\" = unconstrained approach (passed lavaan), \"dblcent\" = double centering approach (passed lavaan), \"pind\" = prod ind approach, constraints centering (passed lavaan), \"custom\" = use parameters specified function call (passed lavaan) match product indicators created using match-strategy standardize.data data scaled fitting model center.data data centered fitting model first.loading.fixed first factor loading latent product fixed one? center.indicators products centered computing products (overwritten method, method != NULL) center.indicator products centered computed? residuals.prods indicator products centered using residuals (overwritten method, method != NULL) residual.cov.syntax syntax residual covariances produced (overwritten method, method != NULL) constrained.prod.mean syntax product mean produced (overwritten method, method != NULL) constrained.loadings syntax constrained loadings produced (overwritten method, method != NULL) constrained.var syntax constrained variances produced (overwritten method, method != NULL) constrained.res.cov.method method constraining residual covariances auto.scale methods scaled automatically (usually useful) auto.center methods centered automatically (usually useful) estimator estimator use lavaan group group variable multigroup analysis run model run via lavaan, FALSE modified syntax data returned suppress.warnings.lavaan warnings lavaan suppressed? ... arguments passed functions, e.g., lavaan","code":""},{"path":"/reference/modsem_pi.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Interaction between latent variables using product indicators — modsem_pi","text":"modsem object","code":""},{"path":"/reference/modsem_pi.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Interaction between latent variables using product indicators — modsem_pi","text":"","code":"library(modsem) # For more examples, check README and/or GitHub. # One interaction m1 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' # Double centering approach est1 <- modsem_pi(m1, oneInt) summary(est1) #> modsem: #> Method = dblcent #> lavaan 0.6-19 ended normally after 159 iterations #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 60 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 122.924 #> Degrees of freedom 111 #> P-value (Chi-square) 0.207 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Latent Variables: #> Estimate Std.Err z-value P(>|z|) #> X =~ #> x1 1.000 #> x2 0.804 0.013 63.612 0.000 #> x3 0.916 0.014 67.144 0.000 #> Y =~ #> y1 1.000 #> y2 0.798 0.007 107.428 0.000 #> y3 0.899 0.008 112.453 0.000 #> Z =~ #> z1 1.000 #> z2 0.812 0.013 64.763 0.000 #> z3 0.882 0.013 67.014 0.000 #> XZ =~ #> x1z1 1.000 #> x2z1 0.805 0.013 60.636 0.000 #> x3z1 0.877 0.014 62.680 0.000 #> x1z2 0.793 0.013 59.343 0.000 #> x2z2 0.646 0.015 43.672 0.000 #> x3z2 0.706 0.016 44.292 0.000 #> x1z3 0.887 0.014 63.700 0.000 #> x2z3 0.716 0.016 45.645 0.000 #> x3z3 0.781 0.017 45.339 0.000 #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> Y ~ #> X 0.675 0.027 25.379 0.000 #> Z 0.561 0.026 21.606 0.000 #> XZ 0.702 0.027 26.360 0.000 #> #> Covariances: #> Estimate Std.Err z-value P(>|z|) #> .x1z1 ~~ #> .x2z2 0.000 #> .x2z3 0.000 #> .x3z2 0.000 #> .x3z3 0.000 #> .x2z1 ~~ #> .x1z2 0.000 #> .x1z2 ~~ #> .x2z3 0.000 #> .x3z1 ~~ #> .x1z2 0.000 #> .x1z2 ~~ #> .x3z3 0.000 #> .x2z1 ~~ #> .x1z3 0.000 #> .x2z2 ~~ #> .x1z3 0.000 #> .x3z1 ~~ #> .x1z3 0.000 #> .x3z2 ~~ #> .x1z3 0.000 #> .x2z1 ~~ #> .x3z2 0.000 #> .x3z3 0.000 #> .x3z1 ~~ #> .x2z2 0.000 #> .x2z2 ~~ #> .x3z3 0.000 #> .x3z1 ~~ #> .x2z3 0.000 #> .x3z2 ~~ #> .x2z3 0.000 #> .x1z1 ~~ #> .x1z2 0.115 0.008 14.802 0.000 #> .x1z3 0.114 0.008 13.947 0.000 #> .x2z1 0.125 0.008 16.095 0.000 #> .x3z1 0.140 0.009 16.135 0.000 #> .x1z2 ~~ #> .x1z3 0.103 0.007 14.675 0.000 #> .x2z2 0.128 0.006 20.850 0.000 #> .x3z2 0.146 0.007 21.243 0.000 #> .x1z3 ~~ #> .x2z3 0.116 0.007 17.818 0.000 #> .x3z3 0.135 0.007 18.335 0.000 #> .x2z1 ~~ #> .x2z2 0.135 0.006 20.905 0.000 #> .x2z3 0.145 0.007 21.145 0.000 #> .x3z1 0.114 0.007 16.058 0.000 #> .x2z2 ~~ #> .x2z3 0.117 0.006 20.419 0.000 #> .x3z2 0.116 0.006 20.586 0.000 #> .x2z3 ~~ #> .x3z3 0.109 0.006 18.059 0.000 #> .x3z1 ~~ #> .x3z2 0.138 0.007 19.331 0.000 #> .x3z3 0.158 0.008 20.269 0.000 #> .x3z2 ~~ #> .x3z3 0.131 0.007 19.958 0.000 #> X ~~ #> Z 0.201 0.024 8.271 0.000 #> XZ 0.016 0.025 0.628 0.530 #> Z ~~ #> XZ 0.062 0.025 2.449 0.014 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .x1 0.160 0.009 17.871 0.000 #> .x2 0.162 0.007 22.969 0.000 #> .x3 0.163 0.008 20.161 0.000 #> .y1 0.159 0.009 17.896 0.000 #> .y2 0.154 0.007 22.640 0.000 #> .y3 0.164 0.008 20.698 0.000 #> .z1 0.168 0.009 18.143 0.000 #> .z2 0.158 0.007 22.264 0.000 #> .z3 0.158 0.008 20.389 0.000 #> .x1z1 0.311 0.014 22.227 0.000 #> .x2z1 0.292 0.011 27.287 0.000 #> .x3z1 0.327 0.012 26.275 0.000 #> .x1z2 0.290 0.011 26.910 0.000 #> .x2z2 0.239 0.008 29.770 0.000 #> .x3z2 0.270 0.009 29.117 0.000 #> .x1z3 0.272 0.012 23.586 0.000 #> .x2z3 0.245 0.009 27.979 0.000 #> .x3z3 0.297 0.011 28.154 0.000 #> X 0.981 0.036 26.895 0.000 #> .Y 0.990 0.038 25.926 0.000 #> Z 1.016 0.038 26.856 0.000 #> XZ 1.045 0.044 24.004 0.000 #> if (FALSE) { # \\dontrun{ # The Constrained Approach est1Constrained <- modsem_pi(m1, oneInt, method = \"ca\") summary(est1Constrained) } # } # Theory Of Planned Behavior tpb <- ' # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) # Covariances ATT ~~ SN + PBC PBC ~~ SN # Causal Relationships INT ~ ATT + SN + PBC BEH ~ INT + PBC BEH ~ INT:PBC ' # Double centering approach estTpb <- modsem_pi(tpb, data = TPB) summary(estTpb) #> modsem: #> Method = dblcent #> lavaan 0.6-19 ended normally after 169 iterations #> #> Estimator ML #> Optimization method NLMINB #> Number of model parameters 78 #> #> Number of observations 2000 #> #> Model Test User Model: #> #> Test statistic 207.615 #> Degrees of freedom 222 #> P-value (Chi-square) 0.747 #> #> Parameter Estimates: #> #> Standard errors Standard #> Information Expected #> Information saturated (h1) model Structured #> #> Latent Variables: #> Estimate Std.Err z-value P(>|z|) #> ATT =~ #> att1 1.000 #> att2 0.878 0.012 71.509 0.000 #> att3 0.789 0.012 66.368 0.000 #> att4 0.695 0.011 61.017 0.000 #> att5 0.887 0.013 70.884 0.000 #> SN =~ #> sn1 1.000 #> sn2 0.889 0.017 52.553 0.000 #> PBC =~ #> pbc1 1.000 #> pbc2 0.912 0.013 69.500 0.000 #> pbc3 0.801 0.012 65.830 0.000 #> INT =~ #> int1 1.000 #> int2 0.914 0.016 58.982 0.000 #> int3 0.808 0.015 55.547 0.000 #> BEH =~ #> b1 1.000 #> b2 0.960 0.030 31.561 0.000 #> INTPBC =~ #> int1pbc1 1.000 #> int2pbc1 0.931 0.015 63.809 0.000 #> int3pbc1 0.774 0.013 60.107 0.000 #> int1pbc2 0.893 0.013 68.172 0.000 #> int2pbc2 0.826 0.017 48.845 0.000 #> int3pbc2 0.690 0.015 45.300 0.000 #> int1pbc3 0.799 0.012 67.008 0.000 #> int2pbc3 0.738 0.015 47.809 0.000 #> int3pbc3 0.622 0.014 45.465 0.000 #> #> Regressions: #> Estimate Std.Err z-value P(>|z|) #> INT ~ #> ATT 0.213 0.026 8.170 0.000 #> SN 0.177 0.028 6.416 0.000 #> PBC 0.217 0.030 7.340 0.000 #> BEH ~ #> INT 0.191 0.024 7.817 0.000 #> PBC 0.230 0.022 10.507 0.000 #> INTPBC 0.204 0.018 11.425 0.000 #> #> Covariances: #> Estimate Std.Err z-value P(>|z|) #> ATT ~~ #> SN 0.629 0.029 21.977 0.000 #> PBC 0.678 0.029 23.721 0.000 #> SN ~~ #> PBC 0.678 0.029 23.338 0.000 #> .int1pbc1 ~~ #> .int2pbc2 0.000 #> .int2pbc3 0.000 #> .int3pbc2 0.000 #> .int3pbc3 0.000 #> .int2pbc1 ~~ #> .int1pbc2 0.000 #> .int1pbc2 ~~ #> .int2pbc3 0.000 #> .int3pbc1 ~~ #> .int1pbc2 0.000 #> .int1pbc2 ~~ #> .int3pbc3 0.000 #> .int2pbc1 ~~ #> .int1pbc3 0.000 #> .int2pbc2 ~~ #> .int1pbc3 0.000 #> .int3pbc1 ~~ #> .int1pbc3 0.000 #> .int3pbc2 ~~ #> .int1pbc3 0.000 #> .int2pbc1 ~~ #> .int3pbc2 0.000 #> .int3pbc3 0.000 #> .int3pbc1 ~~ #> .int2pbc2 0.000 #> .int2pbc2 ~~ #> .int3pbc3 0.000 #> .int3pbc1 ~~ #> .int2pbc3 0.000 #> .int3pbc2 ~~ #> .int2pbc3 0.000 #> .int1pbc1 ~~ #> .int1pbc2 0.126 0.009 14.768 0.000 #> .int1pbc3 0.102 0.007 13.794 0.000 #> .int2pbc1 0.104 0.007 14.608 0.000 #> .int3pbc1 0.091 0.006 14.109 0.000 #> .int1pbc2 ~~ #> .int1pbc3 0.095 0.007 13.852 0.000 #> .int2pbc2 0.128 0.007 19.320 0.000 #> .int3pbc2 0.119 0.006 19.402 0.000 #> .int1pbc3 ~~ #> .int2pbc3 0.110 0.006 19.911 0.000 #> .int3pbc3 0.097 0.005 19.415 0.000 #> .int2pbc1 ~~ #> .int2pbc2 0.152 0.008 18.665 0.000 #> .int2pbc3 0.138 0.007 18.779 0.000 #> .int3pbc1 0.082 0.006 13.951 0.000 #> .int2pbc2 ~~ #> .int2pbc3 0.121 0.007 18.361 0.000 #> .int3pbc2 0.104 0.005 19.047 0.000 #> .int2pbc3 ~~ #> .int3pbc3 0.087 0.005 19.180 0.000 #> .int3pbc1 ~~ #> .int3pbc2 0.139 0.007 21.210 0.000 #> .int3pbc3 0.123 0.006 21.059 0.000 #> .int3pbc2 ~~ #> .int3pbc3 0.114 0.005 21.021 0.000 #> ATT ~~ #> INTPBC 0.086 0.024 3.519 0.000 #> SN ~~ #> INTPBC 0.055 0.025 2.230 0.026 #> PBC ~~ #> INTPBC 0.087 0.024 3.609 0.000 #> #> Variances: #> Estimate Std.Err z-value P(>|z|) #> .att1 0.167 0.007 23.528 0.000 #> .att2 0.150 0.006 24.693 0.000 #> .att3 0.160 0.006 26.378 0.000 #> .att4 0.163 0.006 27.649 0.000 #> .att5 0.159 0.006 24.930 0.000 #> .sn1 0.178 0.015 12.110 0.000 #> .sn2 0.156 0.012 13.221 0.000 #> .pbc1 0.145 0.008 18.440 0.000 #> .pbc2 0.160 0.007 21.547 0.000 #> .pbc3 0.154 0.007 23.716 0.000 #> .int1 0.158 0.009 18.152 0.000 #> .int2 0.160 0.008 20.345 0.000 #> .int3 0.167 0.007 23.414 0.000 #> .b1 0.186 0.018 10.058 0.000 #> .b2 0.135 0.017 8.080 0.000 #> .int1pbc1 0.266 0.013 20.971 0.000 #> .int2pbc1 0.292 0.012 24.421 0.000 #> .int3pbc1 0.251 0.010 26.305 0.000 #> .int1pbc2 0.290 0.012 24.929 0.000 #> .int2pbc2 0.269 0.010 26.701 0.000 #> .int3pbc2 0.253 0.009 29.445 0.000 #> .int1pbc3 0.223 0.009 24.431 0.000 #> .int2pbc3 0.234 0.008 27.633 0.000 #> .int3pbc3 0.203 0.007 29.288 0.000 #> ATT 0.998 0.037 27.138 0.000 #> SN 0.987 0.039 25.394 0.000 #> PBC 0.962 0.035 27.260 0.000 #> .INT 0.490 0.020 24.638 0.000 #> .BEH 0.455 0.023 20.068 0.000 #> INTPBC 1.020 0.041 24.612 0.000 #> if (FALSE) { # \\dontrun{ # The Constrained Approach estTpbConstrained <- modsem_pi(tpb, data = TPB, method = \"ca\") summary(estTpbConstrained) } # }"},{"path":"/reference/modsemify.html","id":null,"dir":"Reference","previous_headings":"","what":"Generate parameter table for lavaan syntax — modsemify","title":"Generate parameter table for lavaan syntax — modsemify","text":"Generate parameter table lavaan syntax","code":""},{"path":"/reference/modsemify.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Generate parameter table for lavaan syntax — modsemify","text":"","code":"modsemify(syntax)"},{"path":"/reference/modsemify.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Generate parameter table for lavaan syntax — modsemify","text":"syntax model syntax","code":""},{"path":"/reference/modsemify.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Generate parameter table for lavaan syntax — modsemify","text":"data.frame columns lhs, op, rhs, mod","code":""},{"path":"/reference/modsemify.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Generate parameter table for lavaan syntax — modsemify","text":"","code":"library(modsem) m1 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' modsemify(m1) #> lhs op rhs mod #> 1 X =~ x1 #> 2 X =~ x2 #> 3 X =~ x3 #> 4 Y =~ y1 #> 5 Y =~ y2 #> 6 Y =~ y3 #> 7 Z =~ z1 #> 8 Z =~ z2 #> 9 Z =~ z3 #> 10 Y ~ X #> 11 Y ~ Z #> 12 Y ~ X:Z"},{"path":"/reference/multiplyIndicatorsCpp.html","id":null,"dir":"Reference","previous_headings":"","what":"Multiply indicators — multiplyIndicatorsCpp","title":"Multiply indicators — multiplyIndicatorsCpp","text":"Multiply indicators","code":""},{"path":"/reference/multiplyIndicatorsCpp.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Multiply indicators — multiplyIndicatorsCpp","text":"","code":"multiplyIndicatorsCpp(df)"},{"path":"/reference/multiplyIndicatorsCpp.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Multiply indicators — multiplyIndicatorsCpp","text":"df data DataFrame","code":""},{"path":"/reference/multiplyIndicatorsCpp.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Multiply indicators — multiplyIndicatorsCpp","text":"NumericVector","code":""},{"path":"/reference/oneInt.html","id":null,"dir":"Reference","previous_headings":"","what":"oneInt — oneInt","title":"oneInt — oneInt","text":"simulated dataset one interaction effect","code":""},{"path":"/reference/parameter_estimates.html","id":null,"dir":"Reference","previous_headings":"","what":"Extract parameterEstimates from an estimated model — parameter_estimates","title":"Extract parameterEstimates from an estimated model — parameter_estimates","text":"Extract parameterEstimates estimated model","code":""},{"path":"/reference/parameter_estimates.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Extract parameterEstimates from an estimated model — parameter_estimates","text":"","code":"parameter_estimates(object, ...)"},{"path":"/reference/parameter_estimates.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Extract parameterEstimates from an estimated model — parameter_estimates","text":"object object class modsem_pi, modsem_da, modsem_mplus ... Additional arguments passed functions","code":""},{"path":"/reference/plot_interaction.html","id":null,"dir":"Reference","previous_headings":"","what":"Plot Interaction Effects — plot_interaction","title":"Plot Interaction Effects — plot_interaction","text":"Plot Interaction Effects","code":""},{"path":"/reference/plot_interaction.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Plot Interaction Effects — plot_interaction","text":"","code":"plot_interaction( x, z, y, xz = NULL, vals_x = seq(-3, 3, 0.001), vals_z, model, alpha_se = 0.15, ... )"},{"path":"/reference/plot_interaction.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Plot Interaction Effects — plot_interaction","text":"x name variable x-axis z name moderator variable y name outcome variable xz name interaction term. interaction term specified, created using x z. vals_x values x variable plot, values smoother std.error-area vals_z values moderator variable plot. separate regression line (y ~ x | z) plotted value moderator variable model object class modsem_pi, modsem_da, modsem_mplus alpha_se alpha level std.error area ... Additional arguments passed functions","code":""},{"path":"/reference/plot_interaction.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Plot Interaction Effects — plot_interaction","text":"ggplot object","code":""},{"path":"/reference/plot_interaction.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Plot Interaction Effects — plot_interaction","text":"","code":"library(modsem) if (FALSE) { # \\dontrun{ m1 <- \" # Outer Model X =~ x1 X =~ x2 + x3 Z =~ z1 + z2 + z3 Y =~ y1 + y2 + y3 # Inner model Y ~ X + Z + X:Z \" est1 <- modsem(m1, data = oneInt) plot_interaction(\"X\", \"Z\", \"Y\", \"X:Z\", -3:3, c(-0.2, 0), est1) tpb <- \" # Outer Model (Based on Hagger et al., 2007) ATT =~ att1 + att2 + att3 + att4 + att5 SN =~ sn1 + sn2 PBC =~ pbc1 + pbc2 + pbc3 INT =~ int1 + int2 + int3 BEH =~ b1 + b2 # Inner Model (Based on Steinmetz et al., 2011) # Causal Relationsships INT ~ ATT + SN + PBC BEH ~ INT + PBC # BEH ~ ATT:PBC BEH ~ PBC:INT # BEH ~ PBC:PBC \" est2 <- modsem(tpb, TPB, method = \"lms\") plot_interaction(x = \"INT\", z = \"PBC\", y = \"BEH\", xz = \"PBC:INT\", vals_z = c(-0.5, 0.5), model = est2) } # }"},{"path":"/reference/standardized_estimates.html","id":null,"dir":"Reference","previous_headings":"","what":"Get standardized estimates — standardized_estimates","title":"Get standardized estimates — standardized_estimates","text":"Get standardized estimates","code":""},{"path":"/reference/standardized_estimates.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Get standardized estimates — standardized_estimates","text":"","code":"standardized_estimates(object, ...)"},{"path":"/reference/standardized_estimates.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Get standardized estimates — standardized_estimates","text":"object object class modsem_da, modsem_mplus, parTable class data.frame ... Additional arguments passed functions","code":""},{"path":"/reference/standardized_estimates.html","id":"details","dir":"Reference","previous_headings":"","what":"Details","title":"Get standardized estimates — standardized_estimates","text":"modsem_da, modsem_mplus objects, interaction term standardized var(xz) = 1. interaction term actual variable model, meaning variance. must therefore calculated parameters model. Assuming normality zero-means, variance calculated var(xz) = var(x) * var(z) + cov(x, z)^2. Thus setting variance interaction term 1 'correct' correlation x z zero. means standardized estimates interaction term different using lavaan, since interaction term actual latent variable model, standardized variance 1.","code":""},{"path":"/reference/summary.html","id":null,"dir":"Reference","previous_headings":"","what":"summary for modsem objects — summary.modsem_da","title":"summary for modsem objects — summary.modsem_da","text":"summary modsem objects summary modsem objects summary modsem objects","code":""},{"path":"/reference/summary.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"summary for modsem objects — summary.modsem_da","text":"","code":"# S3 method for class 'modsem_da' summary( object, H0 = TRUE, verbose = TRUE, r.squared = TRUE, adjusted.stat = FALSE, digits = 3, scientific = FALSE, ci = FALSE, standardized = FALSE, loadings = TRUE, regressions = TRUE, covariances = TRUE, intercepts = TRUE, variances = TRUE, var.interaction = FALSE, ... ) # S3 method for class 'modsem_mplus' summary( object, scientific = FALSE, standardize = FALSE, ci = FALSE, digits = 3, loadings = TRUE, regressions = TRUE, covariances = TRUE, intercepts = TRUE, variances = TRUE, ... ) # S3 method for class 'modsem_pi' summary(object, ...)"},{"path":"/reference/summary.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"summary for modsem objects — summary.modsem_da","text":"object modsem object summarized H0 null model estimated (used comparison) verbose print progress estimation null model r.squared calculate R-squared adjusted.stat sample size corrected/adjustes AIC BIC reported? digits number digits print scientific print p-values scientific notation ci print confidence intervals standardized print standardized estimates loadings print loadings regressions print regressions covariances print covariances intercepts print intercepts variances print variances var.interaction FALSE (default) variances interaction terms removed (present) ... arguments passed lavaan::summary() standardize standardize estimates","code":""},{"path":"/reference/summary.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"summary for modsem objects — summary.modsem_da","text":"","code":"if (FALSE) { # \\dontrun{ m1 <- \" # Outer Model X =~ x1 + x2 + x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z \" est1 <- modsem(m1, oneInt, \"qml\") summary(est1, ci = TRUE, scientific = TRUE) } # }"},{"path":"/reference/trace_path.html","id":null,"dir":"Reference","previous_headings":"","what":"Estimate formulas for (co-)variance paths using Wright's path tracing rules — trace_path","title":"Estimate formulas for (co-)variance paths using Wright's path tracing rules — trace_path","text":"function estimates path x y using path tracing rules. Note works structural parameters, \"=~\" ignored, unless measurement.model = TRUE. want use measurement model, \"~\" mod column pt.","code":""},{"path":"/reference/trace_path.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Estimate formulas for (co-)variance paths using Wright's path tracing rules — trace_path","text":"","code":"trace_path( pt, x, y, parenthesis = TRUE, missing.cov = FALSE, measurement.model = FALSE, maxlen = 100, ... )"},{"path":"/reference/trace_path.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Estimate formulas for (co-)variance paths using Wright's path tracing rules — trace_path","text":"pt data frame columns lhs, op, rhs, mod, modsemify x Source variable y Destination variable parenthesis TRUE, output enclosed parenthesis missing.cov TRUE, covariances missing model syntax added measurement.model TRUE, function use measurement model maxlen Maximum length path aborting ... Additional arguments passed trace_path","code":""},{"path":"/reference/trace_path.html","id":"value","dir":"Reference","previous_headings":"","what":"Value","title":"Estimate formulas for (co-)variance paths using Wright's path tracing rules — trace_path","text":"string estimated path (simplified possible)","code":""},{"path":"/reference/trace_path.html","id":"ref-examples","dir":"Reference","previous_headings":"","what":"Examples","title":"Estimate formulas for (co-)variance paths using Wright's path tracing rules — trace_path","text":"","code":"library(modsem) m1 <- ' # Outer Model X =~ x1 + x2 +x3 Y =~ y1 + y2 + y3 Z =~ z1 + z2 + z3 # Inner model Y ~ X + Z + X:Z ' pt <- modsemify(m1) trace_path(pt, x = \"Y\", y = \"Y\", missing.cov = TRUE) # variance of Y #> [1] \"(X~~X * Y~X ^ 2 + 2 * X~~Z * Y~X * Y~Z + Y~Z ^ 2 * Z~~Z + Y~~Y)\""},{"path":"/reference/var_interactions.html","id":null,"dir":"Reference","previous_headings":"","what":"Extract or modify parTable from an estimated model with estimated variances of interaction terms — var_interactions","title":"Extract or modify parTable from an estimated model with estimated variances of interaction terms — var_interactions","text":"Extract modify parTable estimated model estimated variances interaction terms","code":""},{"path":"/reference/var_interactions.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Extract or modify parTable from an estimated model with estimated variances of interaction terms — var_interactions","text":"","code":"var_interactions(object, ...)"},{"path":"/reference/var_interactions.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Extract or modify parTable from an estimated model with estimated variances of interaction terms — var_interactions","text":"object object class modsem_da, modsem_mplus, parTable class data.frame ... Additional arguments passed functions","code":""},{"path":"/reference/vcov_modsem_da.html","id":null,"dir":"Reference","previous_headings":"","what":"Wrapper for vcov — vcov_modsem_da","title":"Wrapper for vcov — vcov_modsem_da","text":"wrapper vcov, used modsem::vcov_modsem_da, since vcov namespace modsem, stats","code":""},{"path":"/reference/vcov_modsem_da.html","id":"ref-usage","dir":"Reference","previous_headings":"","what":"Usage","title":"Wrapper for vcov — vcov_modsem_da","text":"","code":"vcov_modsem_da(object, ...)"},{"path":"/reference/vcov_modsem_da.html","id":"arguments","dir":"Reference","previous_headings":"","what":"Arguments","title":"Wrapper for vcov — vcov_modsem_da","text":"object fittet model inspect ... additional arguments","code":""}]