Dear all,

I've gotten myself in terrible trouble with a very complicated model specification which includes an individual-level interaction tested for 36,000 Individuals nested in 33 countries for which I would like to know whether it varies between two country groups.

For the first step I am estimating the individual-level main effects and interaction term on the dependent variable with random slopes for main effects and the interaction:

mixed dv main1 main2 main1Xmain2 || country: main1 main2 main1Xmain2, cov(un) mle

and I am pretty sure that I need to have random slopes for both main effects and the interaction because later on I want to know whether the interaction is stronger in the two country sub-groups (e.g. richer societies vs poorer societies).

For this second step my first approach was to simply split up the sample in two groups (e.g. 17 poor countries and 16 rich countries) and rerun the same model for the two groups:

mixed dv main1 main2 main1Xmain2 if poor==0 || country: main1 main2 main1Xmain2, cov(un) mle
mixed dv main1 main2 main1Xmain2 if poor==1 || country: main1 main2 main1Xmain2, cov(un) mle

However, I have no idea how to compare whether the interaction effects differ significantly because I don't know how to calculate confidence intervals for interactions with random slopes (is that even possible?).

My second approach thus was to estimate a three way interaction - including the country level variable main3 (which I used above to split the sample in poor==0 and poor==1) - following the UCLA instruction (https://stats.idre.ucla.edu/stata/fa...tion-stata-12/) which then looked like this:

mixed dv main1 main2 main3 main1Xmain2 main1Xmain3 main2Xmain3 main1Xmain2Xmain3 || country: main1 main2 main1Xmain2, cov(un) mle

and did not converge (Hessian is not negative semidefinite).

Anyway I would not have prefered this latter model because I think three-way-interactions are terrible to interpret.

I would very much like to stick with my first approach (comparing two country sub-samples) but therefore I would need some way of comparing whether the whole interaction effect in the one group is significantly different from that in the other group.

Any ideas are highly welcome!

Thank you all very much in advance for your input!
Leonie