Composite Constructs
As of version 1.0.20, the modsem function
supports the estimation of models with composite constructs, when using
method="lms". The approach is based on Tamara Schamberger, Florian
Schuberth, Jörg Henseler & Yves Rosseel, 2015. Depending on your
lavaan version (>=0.6-20), composite
constructs can also be used with the product indicator approaches (e.g.,
method="dblcent").
Here we can see a simple example, using the LMS approach with the
TPB dataset.
tpb <- '
# Outer Model (Based on Hagger et al., 2007)
# Latent Variables
SN =~ sn1 + sn2
PBC =~ pbc1 + pbc2 + pbc3
INT =~ int1 + int2 + int3
# Composites
ATT <~ att1 + att2 + att3 + att4 + att5
BEH <~ b1 + b2
# Inner Model (Based on Steinmetz et al., 2011)
INT ~ ATT + SN + PBC
BEH ~ INT + PBC + INT:PBC
'
fit <- modsem(tpb, TPB, method = "lms", nodes = 32)
summary(fit)
#>
#> modsem (1.0.21) ended normally after 67 iterations
#>
#> Estimator LMS
#> Optimization method EMA-NLMINB
#> Number of model parameters 47
#>
#> Number of observations 2000
#>
#> Loglikelihood and Information Criteria:
#> Loglikelihood -26324.39
#> Akaike (AIC) 52742.78
#> Bayesian (BIC) 53006.02
#>
#> Numerical Integration:
#> Points of integration (per dim) 32
#> Dimensions 1
#> Total points of integration 32
#>
#> Fit Measures for Baseline Model (H0):
#> Standard
#> Chi-square 63.05
#> Degrees of Freedom (Chi-square) 71
#> P-value (Chi-square) 0.738
#> RMSEA 0.000
#>
#> Loglikelihood -26391.61
#> Akaike (AIC) 52875.22
#> Bayesian (BIC) 53132.86
#>
#> Comparative Fit to H0 (LRT test):
#> Loglikelihood change 67.22
#> Difference test (D) 134.44
#> Degrees of freedom (D) 1
#> P-value (D) 0.000
#>
#> R-Squared Interaction Model (H1):
#> INT 0.364
#> BEH 0.232
#> R-Squared Baseline Model (H0):
#> INT 0.364
#> BEH 0.186
#> R-Squared Change (H1 - H0):
#> INT 0.000
#> BEH 0.046
#>
#> Parameter Estimates:
#> Coefficients unstandardized
#> Information observed
#> Standard errors standard
#>
#> Latent Variables:
#> Estimate Std.Error z.value P(>|z|)
#> SN =~
#> sn1 1.000
#> sn2 0.888 0.017 52.434 0.000
#> PBC =~
#> pbc1 1.000
#> pbc2 0.912 0.013 69.250 0.000
#> pbc3 0.801 0.012 65.957 0.000
#> INT =~
#> int1 1.000
#> int2 0.913 0.015 58.975 0.000
#> int3 0.807 0.014 55.678 0.000
#>
#> Composites:
#> Estimate Std.Error z.value P(>|z|)
#> ATT <~
#> att1 1.000
#> att2 0.674 0.289 2.329 0.020
#> att3 0.872 0.314 2.773 0.006
#> att4 0.840 0.304 2.763 0.006
#> att5 1.119 0.359 3.115 0.002
#> BEH <~
#> b1 1.000
#> b2 1.355 0.352 3.848 0.000
#>
#> Regressions:
#> Estimate Std.Error z.value P(>|z|)
#> INT ~
#> SN 0.182 0.027 6.611 0.000
#> PBC 0.226 0.029 7.766 0.000
#> ATT 0.051 0.013 4.038 0.000
#> BEH ~
#> PBC 0.535 0.092 5.795 0.000
#> INT 0.436 0.087 4.990 0.000
#> INT:PBC 0.471 0.079 5.940 0.000
#>
#> Intercepts:
#> Estimate Std.Error z.value P(>|z|)
#> .pbc1 0.997 0.024 42.396 0.000
#> .pbc2 0.985 0.022 44.917 0.000
#> .pbc3 0.991 0.020 50.438 0.000
#> .sn1 1.005 0.024 41.645 0.000
#> .sn2 1.010 0.022 46.693 0.000
#> att1 1.014 0.024 41.986 0.000
#> att2 1.007 0.021 46.946 0.000
#> att3 1.016 0.020 51.433 0.000
#> att4 0.999 0.018 55.631 0.000
#> att5 0.992 0.022 45.651 0.000
#> .int1 1.014 0.022 46.943 0.000
#> .int2 1.012 0.020 50.385 0.000
#> .int3 1.005 0.018 54.786 0.000
#> b1 1.001 0.021 47.006 0.000
#> b2 1.019 0.020 51.074 0.000
#>
#> Covariances:
#> Estimate Std.Error z.value P(>|z|)
#> att2 ~~
#> att1 0.878
#> att3 ~~
#> att1 0.788
#> att2 0.692
#> att4 ~~
#> att1 0.693
#> att2 0.609
#> att3 0.547
#> att5 ~~
#> att1 0.885
#> att2 0.778
#> att3 0.698
#> att4 0.616
#> b2 ~~
#> b1 0.605
#> SN ~~
#> ATT 2.431 0.530 4.588 0.000
#> PBC ~~
#> SN 0.678 0.029 23.331 0.000
#> ATT 2.620 0.571 4.590 0.000
#>
#> Variances:
#> Estimate Std.Error z.value P(>|z|)
#> .pbc1 0.144 0.008 18.090 0.000
#> .pbc2 0.160 0.008 21.192 0.000
#> .pbc3 0.155 0.007 23.675 0.000
#> .sn1 0.178 0.015 12.011 0.000
#> .sn2 0.157 0.012 13.189 0.000
#> att1 1.166
#> att2 0.920
#> att3 0.781
#> att4 0.645
#> att5 0.944
#> .int1 0.157 0.009 18.033 0.000
#> .int2 0.160 0.008 20.331 0.000
#> .int3 0.168 0.007 23.465 0.000
#> b1 0.815
#> b2 0.716
#> SN 0.988 0.039 25.373 0.000
#> PBC 0.963 0.035 27.239 0.000
#> ATT 15.508 6.651 2.332 0.020
#> .INT 0.493 0.020 24.660 0.000
#> .BEH 2.845 0.844 3.372 0.001