I was hoping you could provide some information on how one should interpret and present group level coefficients and degrees of freedom in a mixed effects (in my case: logistic) model. I'm fully aware of how we understand them in the classical sense, certainly in conventional OLS and logistic regression models. However, I have yet to come across a very thorough treatment in most handbooks dedicated to mixed effects modeling (Gelman and Hill, for example). In fact, most seem to be fixated on the level-one (or individual level) predictors and treat level-two (or group level) predictors more as "things you can also do", for which there are usually only one or two pedagogical examples.
My issue is that I have a mixed effects logit model with a number of group predictors, most of which constitute the hypotheses of interest relevant to my research question. I have fifteen group predictors and one random effect for the group ($j = 59$), with over 60,000 total observations at the individual level. I have one group level variable for a hypothesis of interest, for which the $p$-value varies from .06 to .05, contingent on the model specification. Estimating the model using the glmmPQL function in
R (for example) says the DF for the group level variables is $43$ (that is: $59 - 15 - 1$).
If so, would I be able to present the results for that particular variable as significant at .1, given that the group level variables are estimating group averages, for which there is a significantly smaller $N$? Or is there more to understanding group-level coefficients in a mixed effects model than that?
My apologies for any confusion in my question and appreciate any input you may have.