Reading the interesting post Interpretation of variance in multilevel logistic regression I understood that I cannot compare multilevel logistic models looking at the empty model and at variance reductions (as I would have done in multilevel models with a continuous dependent variable).
The suggestion is therefore to use AIC and BIC to make the comparison. In my case study I have about 20 groups and 18,000 observations (nested in groups). AIC and BIC for the empty model are both about 18,600. In the full model (where I add predictors) I obtain a reduction of AIC and BIC of about 1,000 (they are now about 17,650).
Can you help me quantify this reduction? Is it small or large? What are the general rules for assessing the reduction size of AIC and BIC in multilevel logit model, i.e. to say if they are big or small?
Lastly, running these models in Stata, is there any way to have a % measure of the variance explained? and of the effect size of each predictor?