I am working on a set given to me, which involves fitting logistic models with a couple of predictors, some of which are nearly perfectly correlated (.9), imagine, face features deviations of specific genders are highly correlated to deviation of these features in the general population as well s with each other. In this case, two of these at are time or all need to be included in a mixed model as predictors, as arguably they are tied to specific theoretical predictions
I am trying to assess the impact of this collinearity on my results and wonder if model comparison (likelihood ratio test, AIC and BIC and other model fit comparisons) can be a practical solution for addressing this. It is my understanding that model fit should not in general be affected by collinearity, I am thinking building a few different models including and excluding the collinear terms, as well as including or excluding their interactions. I'll end up with a few few maximal and nested models where LRT seems plausible, or using information criteria for the non nested models. Appreciate any thoughts and alternatives.