3-way multi-level interactions... random intercept or random slopes?

[John Ez]

Dear Statalist,

I have data for individuals (level 1) nested within countries (level 2). I'm interested in estimating how country-level (L21) characteristics moderate the interaction effects between two individual level continuous covariates (L11 x L12). What's the best way to model this situation? I find the discussions divided on incorporating random slopes. If so, I'm unclear what random slopes I should incorporate. Which of the following specifications would be the best?

mixed Y L11##L12##L21 || country:, robust

mixed Y L11##L12##L21 || country: L21, robust

mixed Y L11##L12##L21 || country: L11 L12, robust

mixed Y L11##L12##L21 || country: L11#L12, robust (which is not a possible syntax in stata 15 that I'm using)

I'm interested in making inferences in the form of: the interaction effects would increase by x units, as L21 increases by one unit. I'm also not interesting in the effect of L21 on its own, but only as a moderator. So, I'm looking for the simplest way to understand these moderating effects.

I would appreciate your answers. Thanks!

[Marcos Almeida]

Welcome to the Stata Forum / Statalist,

This is all about modeling. It is up to you to do the modeling and only then make a decision.

(By the way, you can create interaction terms when it is "not possible in Stata"").

In short, you need to compare models and check which one "fits" better.

After that, I recommend to use margins and marginsplot to visualize the results.

Just a caveat: in most of the cases I tried this approach, I realized that the "best" model is not necessary the one with "everything" inside.

[John Ez]

Thanks a lot Marcos for your response.

I guess one question I had is: In the case of applying a random slope model, is model (3) the more sensible one as it contains random slopes for the two terms constituting the interaction term? My concern about the last specification is that the random slopes are for the interaction term only, which usually cannot be understood without incorporating information about the components.

[Marcos Almeida]

As I remarked, the best model (‘sensitive’, if you wish) will probably be the one with the best postestimation results.