To Install
# From CRAN
install.packages("modsem")
# Latest version from GitHub
install.packages("devtools")
devtools::install_github("kss2k/modsem", build_vignettes = TRUE)
Methods/Approaches
There are a number of approaches for estimating interaction effects in SEM. In modsem()
, the method = "method"
argument allows you to choose which to use. Different approaches can be categorized into two groups: Product Indicator (PI) and Distribution Analytic (DA) approaches.
Product Indicator (PI) Approaches:

"ca"
= constrained approach (Algina & Moulder, 2001) Note that constraints can become quite complicated for complex models, particularly when there is an interaction including enodgenous variables. The method can therefore be quite slow.

"uca"
= unconstrained approach (Marsh, 2004) 
"rca"
= residual centering approach (Little et al., 2006) 
"dblcent"
= double centering approach (Marsh., 2013) default

"pind"
= basic product indicator approach (not recommended)
Examples
Elementary Interaction Model (Kenny & Judd, 1984)
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)
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 ~ 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)