Similar to standard regression, one includes an interaction term into the model as a predictor, in addition to the two main effects. If you’ve done this *outside* of JMP, you probably had to create the multiplicative/interaction term manually – JMP is very cool so in Fit Model (and other platforms) it saves you the time of doing that with the “Cross” button –it further centers the terms to create the interaction! However, in SEM, I haven’t (yet) added that time-saving feature (but be on the lookout for the future!). Thus, the easiest way is creating a new formula column (select columns and right-click):
Note that if you want the interaction to be created with mean-centered terms (which is usually desired to avoid multicollinearity), you should first select New Formula Column > Distributional > Center, and then create the product variable with the centered terms.
SEM has what’s called “multiple-group analysis” which enables one to explore if/how effects vary across populations. In a nutshell, the exact same model is fit simultaneously to the samples (2 or more) and one tests moderation effects by forcing certain parameter estimates to be equal across the groups and using a chi-square difference test to see if the constraint led the model to fit significantly worse. We will offer multiple-group analysis in JMP Pro 16.
Both of these approaches are good. One usually recommends #2 when sample sizes for each group are large (definition of "large" depends on how complex the model is), otherwise #1 is the way to go. Although SEM is much more flexible than regression, I’d like to illustrate an example of estimating an interaction in SEM and comparing with Fit Model so you can see the similarities. Running the attached script will show you the Fit Model and SEM results and will compute the interaction term with centered terms. As you can see below, the results are the same:
So, the multiplicative term is the key to testing moderation effects in SEM.