# How to conduct predictor selection in a generalized linear mixed model?

I have 18 predictors in a binary generalized linear mixed model (repeated measurements, over a 1000 subjects). I would like to trim the model a bit and remove some noise and useless predictors. Unfortunately, PROC GLIMMIX does not have any facility to do this. I could not find an R package that would do this (step() function style). If I were to try this manually, say begin with a full model (all predictors in) and do a 'backward selection', what criterion could I use to do this quickly? Could I use, say, p-values? But at what significance level?

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In general predictor selection is a bad thing to do. To help understand why, you may want to read my answer here: algorithms-for-automatic-model-selection. –  gung Oct 25 '12 at 22:55

Rather than using a stepwise procedure, I would fit an L1-regularized model, and discard predictors whose coefficients are effectively forced to be zero. See [Ng 2004].

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That would be great, if I could only find an implementation of it specific for a GLMM. I could just ignore the within-individual clustering (yikes!) and attempt something like what you propose, or something related like the elastic-net procedure and see how well it does in cross-validation. If the within-individual nesting is ignored, then a whole plethora of predictive techniques can be used... my main problem was that I did not want to ignore the within-subject repeated measures. But I guess it wouldn't hurt to see what happens if the analysis is conducted that way. –  user16263 Nov 25 '12 at 18:46
I could think of some options here, but maybe it's better to open another question on what software exists to fit regularized GLMM models (or even better, specifically the kind of GLMM you want, which I think is a logistic regression). –  Jack Tanner Nov 25 '12 at 18:49