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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)

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.