modsem

modsem is an R-package for estimating interaction (i.e., moderation) effects between latent variables in structural equation models (SEMs). See https://www.modsem.org for a tutorial.

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)

Distribution Analytic (DA) Approaches

• "lms" = The Latent Moderated Structural equations (LMS) approach, see the vignette
• "qml" = The Quasi Maximum Likelihood (QML) approach, see the vignette
• "mplus"
  • estimates model through Mplus, if it is installed

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)

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)