I'm working with GLMM and a binomial distribution to find the best model for my biological data. I'm currently writing my PhD and I have some trouble to present my results. I read and learn a lot about GLMM but I don't find a satisfying way to present my results, as I'm not statistician.
I'm using R and the lme4 package. I have different GLMM models, with different random intercepts. I compare them with a likelihood ratio test to find the smaller AIC and check if my variables were significant (by removing them one by one).
I did also cross-validation to show how the different models predicts on "unknown" dataset. My questions are pragmatic:
-> should I display all the models with the AIC values and LRT?
-> should I run a cross-validation for all of them?
-> from the cross-validation, is it ok to only present the result from the AUC roc curves?
-> which other results/parameters would you expect to see?
I know that my questions might be terribly trivial but I need some answers as simple as possible as I'm completely lost.