# What is an appropriate technique for large number of correlated predictor variables with interactions?

I want to allow the effects of a large number of continuous predictor variables to be different depending on which treatment group the individual is a part of.

If I had only three continuous predictor variables (X1, X2, X3), I might fit a linear model like this.

Response ~ Treatment + X1 + X2 + X3 + Treatment*X1, Treatment*X2, Treatment*X3


In this case however, I have a large number of correlated continuous predictor variables. I have used PLS before for problems with correlated predictor variables, but I don't know if PLS can handle interaction terms, or if there is a different "flavor" of PLS for problems like this. (PLS-SEM? Latent Class Analysis? I don't really understand these methods...)

I have considered fitting a PLS model for the subset of the data for each Treatment group, but this doesn't seem like good stats.

I'm also not sure how I will interpret the results, because I have typically relied on effects plots to manually judge the nature of fit interactions, which will be difficult to do with a latent variable approach. Many thanks.