Analyzing categorical and continuous variable interactions in SEM using R's lavaan: Any tips?

CFA
1

I’m trying to set up a structural equation model (SEM) in R using lavaan. My goal is to look at how a categorical variable and a continuous moderator (from a CFA) interact. It’s kind of like doing a two-way ANOVA in SEM, plus testing a moderator with each factor.

Here’s what I’ve tried:

# Quick data setup
library(lavaan)
set.seed(42)
n = 200
data = data.frame(
  outcome = rnorm(n),
  mod1 = rnorm(n), mod2 = rnorm(n), mod3 = rnorm(n),
  factor1 = sample(c('X','Y'), n, replace=TRUE),
  factor2 = sample(c('P','Q'), n, replace=TRUE)
)

# Basic model works fine
model1 = '
  moderator =~ mod1 + mod2 + mod3
  outcome ~ factor1 + factor2 + factor1:factor2
'
fit1 = sem(model1, data, meanstructure=TRUE)

# Adding interaction causes issues
model2 = '
  moderator =~ mod1 + mod2 + mod3
  outcome ~ factor1 + factor1:moderator + factor2 + factor1:factor2
'
fit2 = sem(model2, data, meanstructure=TRUE)

The first model runs okay, but the second one with the interaction term throws an error about the variance-covariance matrix.

Is this even possible in lavaan? Are there workarounds? Could Mplus handle this better? Any advice would be great!

2

I’ve encountered this challenge before, and it can be tricky to model interactions between categorical and continuous variables in lavaan. One approach that’s worked for me is using dummy coding for your categorical variables before creating the interaction terms. Here’s a rough outline:

# Dummy code categorical variables
data$factor1_dummy <- as.numeric(data$factor1 == 'Y')
data$factor2_dummy <- as.numeric(data$factor2 == 'Q')

# Create interaction terms
data$factor1_mod <- data$factor1_dummy * data$moderator
data$factor2_mod <- data$factor2_dummy * data$moderator

# Modify your model
model3 <- '
  moderator =~ mod1 + mod2 + mod3
  outcome ~ factor1_dummy + factor2_dummy + moderator + factor1_mod + factor2_mod
'
fit3 <- sem(model3, data, meanstructure=TRUE)

This approach pre-computes the interaction terms, which can help lavaan handle them more easily. Remember to interpret your results carefully, as the coefficients will represent effects relative to the reference categories.

3

hey there! i’ve run into similar issues with lavaan. have you tried using the orthogonalize function from the semTools package? it can help with interaction terms in SEM. something like:

library(semTools)
data_ortho <- orthogonalize(data, 'moderator', c('factor1', 'factor2'))

then use data_ortho in your sem call. might solve the variance-covariance issue. good luck!

4

Hey there, ExploringForest! :slightly_smiling_face:

That’s quite an interesting challenge you’ve got there with lavaan. Have you considered using the semPLS package instead? It’s pretty nifty for handling complex interactions in SEM.

I’m curious, though - what’s the theory behind your model? Sometimes, we get so caught up in the stats that we forget about the ‘why’ behind our analysis. What made you choose these particular variables and interactions?

Oh, and here’s a wild thought - have you tried bootstrapping? It can sometimes help with tricky variance-covariance issues. Maybe something like:

fit2 <- sem(model2, data, meanstructure=TRUE, se='bootstrap', bootstrap=1000)

Just throwing ideas out there! Let me know if any of this helps or if you want to chat more about your research. It sounds fascinating!