Multi-level interaction with fixed reference category - specification and random term structure

[Johannes Muller]

Dear all

I am hoping you may share your advice with me on multi-level interactions.

I am interested in the differences across 2 main groups, G1 and G2.
G2 consists of 100 sub-categories.
The questions I seek to address are
1) whether there are differences across G1 and G2 in predicting a (dichotomous) outcome DV
2) whether a (continuous) predictor at the G2-subcategory level alters the differences between G2 and G1 in predicting the DV.

Because G1 is only one group I cannot estimate a standard interaction model (group*predictor) as far as I can tell. To still shed some light on the issue, I manually create the product of G2 * predictor = G2_predictor and, I then run the model:

logit DV $controls G2 G2_predictor

• Does this make sense?

Given that the predictor only varies at the G2-group-detail level, I seek to account for nesting effects by using multi-level modelling. I can use a group identifier which pools G1 and G2, such that there are 50 G2 groups, 1 G1 group, hence 51 groups in total.

melogit DV $controls G2 G2_predictor || Group12identifer

What concerns me is that this assigns G1 to the same hierarchical level as G2 detail.
Would it make sense to introduce an artificial level such that

melogit DV $controls G2 G2_predictor || G2:  || Group12identifer

Probably not because the G2 dummy is already a fixed part of the model and there are just two groups anyways. But pooling G1 and G2 in Group12identifer doesn't seem correct either.

• What would you recommend?

Thank you very much already in advance!