I am currently looking into how climatic variables affect the breeding success of a bird. In order to do this, I want to compare models for different spatio-temporal regions and compare the models with AICc.

I will be using logistic regression as part of a Generalised Linear Mixed Model (GLMM) as there is a binomial dependent variable called 'chick survival success' (1 = chick survived, 0 = did not survive), random effects ('Year' and 'Nested in Year') so the model knows that the chicks hatching in the same 'year' and chicks which share the same 'nest' share some variance, as well as 1 nominal fixed effect and, for example, 10 covariates.

The 1 fixed nominal effect must be included in every model, however I want to determine what combination of covariates best predicts chick survival success. Instead of running and comparing each and every combination of the 10 covariates alongside the nominal and random variable, I was wondering if there was a way of doing this automatically by adding in all variables on either SPSS or R. I understand there are 'stepwise' methods and 'automated model selection' for GLM and regression models, however I cannot find anything which suggests you can do this for GLMM or when you also have random effects which need to be ran through every model.

Ideally, I'd like to be able to see all of the combinations of variables for each model (or at least the best fitting models) compared to one another using an information criterion. From here, I can determine the best model for each spatio-temporal region and then compare them all to one another.

Any suggestions or help would be greatly appreciated.

Many thanks