I am calculating a two-level linear multilevel analysis. A look at the random intercept random slope model showed me a significant decrease in my model deviance if I include two dummy variables. Those are from a set of 6 dummyvariables in my multilevel model (which was originally a categorical variable with 7 cagegories). The other dummies arent significant (I use the WALD statistics to judge that).
Can I put just those two dummy variables into the random part of my mixed-model or do I have to usw all six dummy variables even though the other four arent significant? Or do I run into any problem with i.e. the reference group of the six dummies or maybe the interpretation of the two dummies?
I googled, I looked into several books, but I do not find an answer to this.
My entities are countries. My dependent variable is a Likert-Scale. My independent variables on the individual level are mostly dummies, i.e. education is split into six dummy categories (with one category as the reference group). The metric variables are grand_mean centered. On the macro level I have four dummy variables (and a refernce group) and two metric grand_mean centered variables. I calculated the empty model with just my dep.V. Then I put everything into the fixed part and after that I tested with the WALD statistics and the lr-test which variables I should let differ across the countries. My first two education categories and one metric variable were significant and I am unsure if I can let just two categories be random.
Does this help? I certainly can show some code but I do not know which part would be helpful.