library(modsem)Both the LMS- and QML approach works on most models, but interaction effects with endogenous can be a bit tricky to estimate (see the vignette. Both approaches (particularily the LMS approach) are quite computationally intensive, and are thus partly implemented in C++ (using Rcpp and RcppArmadillo). Additionally starting parameters are estimated using the double centering approach (and the means of the observed variables) are used to generate good starting parameters for faster convergence. If you want to see the progress of the estimation process you can use ´verbose = TRUE´.
Here you can see an example of the LMS approach for a simple model. By default the summary function calculates fit measures compared to a null model (i.e., the same model without an interaction term).
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 Here you can see the same example using the QML approach.
qml1 <- modsem(m1, oneInt, method = "qml")
summary(qml1)Here you can see an example of a more complicated example using the
model from the theory of planned behaviour (TPB), where there are two
endogenous variables, where there is an interaction between an
endogenous and exogenous variable. When estimating more complicated
models with the LMS-approach, it is recommended that you increase the
number of nodes used for numerical integration. By default the number of
nodes is set to 16, and can be increased using the nodes argument. The
argument has no effect on the QML approach. When there is an interaction
effect between an endogenous and exogenous variable, it is recommended
that you use at least 32 nodes for the LMS-approach. You can also get
robust standard errors by setting robust.se = TRUE in the
modsem() function.
Note: If you want the lms-approach to give as similar results as
possible to mplus, you would have to increase the number of nodes (e.g.,
nodes = 100).
# 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)
qml2 <- modsem(tpb, TPB, method = "qml")
summary(qml2, standardized = TRUE) # standardized estimates