ModSEM

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

To Install

# From CRAN 
install.packages("modsem")

# Latest version from Github
install.packages("devtools")
devtools::install_github("kss2k/modsem")

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.

• "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)
• "lms" = The latent moderated structural equations approach
  • note: now implemented with multiple endogenous variables however it does not allow interactions between two enodgenous variables, it does however allow interactions between exogenous:endogenous and exogenous:exogenous
  • do optimize = TRUE for faster convergence (experimental feature)
• "qml" = The Quasi Maximum Likelihood estimation of latent moderated structural equations.
  • note: only works with a single endogenous variable.
• "mplus"
  • estimates model through Mplus, if it is installed

New Feature (10.04.24)

• Implemented a new estimator for the LMS approach, which now works with more complicated models

Examples

One interaction

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
est1Dblcent <- modsem(m1, oneInt)
summary(est1Dblcent)

# Constrained approach
est1Ca <- modsem(m1, oneInt, method = "ca")
summary(est1Ca)

# QML approach 
est1Qml <- modsem(m1, oneInt, method = "qml")
summary(est1Qml) 

# LMS approach 
est1Lms <- modsem(m1, oneInt, method = "lms") 
summary(est1Lms)

Theory Of Planned Behavior

tpb <- ' 
# Outer Model (Based on Hagger et al., 2007)
  LATT =~ att1 + att2 + att3 + att4 + att5
  LSN =~ sn1 + sn2
  LPBC =~ pbc1 + pbc2 + pbc3
  LINT =~ int1 + int2 + int3
  LBEH =~ b1 + b2

# Inner Model (Based on Steinmetz et al., 2011)
  # Covariances
  LATT ~~ LSN + LPBC
  LPBC ~~ LSN 
  # Causal Relationsships
  LINT ~ LATT + LSN + LPBC
  LBEH ~ LINT + LPBC 
  LBEH ~ LINT:LPBC  
'

# double centering approach
estTpbDblCent <- modsem(tpb, data = TPB, method = "dblcent")
summary(estTpbDblCent)

# Constrained approach using Wrigths path tracing rules for generating
# the appropriate constraints
estTpbCa <- modsem(tpb, data = TPB, method = "ca") 
summary(estTpbCa)

# LMS approach 
estTpbLms <- modsem(tpb, data = TPB, method = "lms")
summary(estTpbLms)

Interactions between two observed variables

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)

Multiple interaction terms

m4 <- '
  # Outer Model
  X =~ x1 + x2 +x3
  Y =~ y1 + y2 + y3
  Z =~ z1 + z2 + z3
  G =~ g1 + g2 + g3
  H =~ h1 + h2 + h3
  
  # Inner model
  Y ~ X + Z + G + H + X:Z + G:H
'

# Using unconstrained approach
est4 <- modsem(m4, twoInt, method = "uca")
summary(est4)

Interactionterms with more than two variables

m5 <- '
  # Outer Model
  X =~ x1 + x2 +x3
  Y =~ y1 + y2 + y3
  Z =~ z1 + z2 + z3
  G =~ g1 + g2 + g3
  
  # Inner model
  Y ~ X + Z + G + X:Z:G
'

# Residual centering approach
est5 <- modsem(m5, tripleInt, standardizeData = TRUE, method = "rca")
summary(est5)