I'm trying to estimate models with three-way interactions in R lavaan using the syntax terms operator : (which works fine with two-way interactions). It seems that lavaan ignores the three-way interaction.
To reproduce the problem, one can use
library(lavaan)
f1<-"y~x1+x2+x3+x1:x2+x2:x3+x1:x2:x3"
lavParseModelString(f1)
$rhs
[1] "x1" "x2" "x3" "x1:x2" "x2:x3"
Am I missing something?
I have only used Lavaan a few times, but have you tried to create the interaction term and inserting it into the model? I am assuming these are observed variables because the ":" works for observed but not latent variables. i.e.,
interaction <- x1*x2*x3
f1 <- "y ~ x1 + x2 + x3 + x1:x2 + x2:x3 + interaction"
I do not know why the ":" does not work for three way interactions. Also, good luck interpreting your three-way interaction!