quadratic effects

In modsem: Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)

EVAL_DEFAULT <- FALSE
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  eval = EVAL_DEFAULT
)

library(modsem)

Quadratic Effects and Interaction Effects

Quadratic effects are essentially a special case of interaction effects—where a variable interacts with itself. As such, all of the methods in modsem can also be used to estimate quadratic effects.

Below is a simple example using the LMS approach.

library(modsem)
m1 <- '
# Outer Model
X =~ x1 + x2 + x3
Y =~ y1 + y2 + y3
Z =~ z1 + z2 + z3

# Inner model
Y ~ X + Z + Z:X + X:X
'

est1Lms <- modsem(m1, data = oneInt, method = "lms")
summary(est1Lms)

In this example, we have a simple model with two quadratic effects and one interaction effect. We estimate the model using both the QML and double-centering approaches, with data from a subset of the PISA 2006 dataset.

m2 <- '
ENJ =~ enjoy1 + enjoy2 + enjoy3 + enjoy4 + enjoy5
CAREER =~ career1 + career2 + career3 + career4
SC =~ academic1 + academic2 + academic3 + academic4 + academic5 + academic6
CAREER ~ ENJ + SC + ENJ:ENJ + SC:SC + ENJ:SC
'

est2Dblcent <- modsem(m2, data = jordan)
est2Qml <- modsem(m2, data = jordan, method = "qml")
summary(est2Qml)

Note: The other approaches (e.g., LMS and constrained methods) can also be used but may be slower depending on the number of interaction effects, especially for the LMS and constrained approaches.

modsem documentation built on April 3, 2025, 7:51 p.m.