How to select automatically the best GLMM? I have a set of 14 variables and I want to construct GLMM's. I want to include at first each variable and then add all the others, one at the time.
This will require a lot of combinations of variables, resulting in many models, and I was wondering if there is a method/R- package that would allow me to select the best models automatically, without having to construct each model "manually"?
 A: Most (if not all) statistical textbooks highly recommend to avoid automatic model selection (there are numerous reasons explained in those books). Instead I recommend you to follow the steps described in the excellent book from Zuur et al. (2009) Mixed Effects Models and Extensions in Ecology with R. 
I won't go into much detail but you'll see that it is recommended to start with the full model (including all explanatory variables and likely significant interactions that you should select) and to remove non-significant explanatory variable or interaction one at the time using for example the drop1 function in R.
A: Rather than trying to add or delete terms based on some noisy criterion such as statistical significance (see, e.g., https://en.wikipedia.org/wiki/Stepwise_regression#Criticism), you will likely be better served by including all 14 variables, which is, after all, not a very large number unless you have a very small sample. If you're worried that most features won't be informative and so this saturated model will readily overfit, try ridge regression or the lasso.
