semTools (version 0.1-0)

orthogonalize: Orthogonalize data for 2-way interaction in SEM

Description

Orthogonalize indicators of a 2-way interaction between latent variables

Usage

orthogonalize(dat, xvars, zvars)

Arguments

dat

Matrix or data frame of item level data.

xvars

A vector of column numbers corresponding to indicators of the focal predictor (x).

zvars

A vector of column numbers corresponding to indicators of the moderator (z).

Value

• 1. data
  Original data with orthogonalized product terms appended.

Details

This functions will take a data frame or matrix and create orthogonalized product terms to compute latent variable interactions based on the method proposed by Little, Bovaird, & Widaman. The orthogonalized product terms can be entered into a SEM as indicators of a latent interaction variable. This function will compute all possible orthogonalized product terms (e.g., x has 3 indicators and z has 4 indicators, the function will return 3*4=12 new orthognalized product terms)

References

Little, T. D., Bovaird, J. A., & Widaman, K. F. (2006). On the merits of orthogonalizing powered and product terms: Implications for modeling interactions among latent variables. Structural Equation Modeling, 13 497-519.

Examples

library(MASS)

n <- 500
means <- c(0,0)
covmat <- matrix(c(1, 0.3, 0.3, 1),nrow=2)

data <- mvrnorm(n,means,covmat)

x<-as.vector(data[,1])
z<-as.vector(data[,2])

y<-rnorm(n,0,1)+.4*x+.4*z+.2*x*z

x1<-rnorm(n,0.2,.2)+.7*x
x2<-rnorm(n,0.2,.2)+.7*x
x3<-rnorm(n,0.2,.2)+.7*x
z1<-rnorm(n,0.2,.2)+.7*z
z2<-rnorm(n,0.2,.2)+.7*z
z3<-rnorm(n,0.2,.2)+.7*z
y1<-rnorm(n,0.2,.2)+.7*y
y2<-rnorm(n,0.2,.2)+.7*y
y3<-rnorm(n,0.2,.2)+.7*y

dat<-data.frame(cbind(x1,x2,x3,z1,z2,z3,y1,y2,y3))

datOrth <-orthogonalize(dat,(1:3), (4:6))

#Fit model in Lavaan
library(lavaan)

syntax <- ' 
x =~ x1 + x2 +x3
z =~ z1 + z2 + z3
xz =~ x1z1 + x1z2 + x1z3 + x2z1 + x2z2 + x2z3 + x3z1 + x3z2 + x3z3
y =~ y1 + y2 + y3
x ~~ z
x ~~ 0*xz
z ~~ 0*xz
y ~ x + z +xz
'

fit <- sem(model = syntax, data=datOrth, std.lv=TRUE)
summary(fit, fit.measures=TRUE)