Hi Birdman. McCullagh and Nelder recommend also using the dispersion scale parameter to compare GL(M)Ms. The closer to unity the better you model and data meet the assumed residual distribution. They also suggest using the (in your case, Generalized) Chi-square(improvement)-to-DOF ratio approximation of same, which GLIMMIX produces. This statistic does not have a formal distribution and so cannot be used in a significance test of improvement with a P-value, but still can be used to identify models that, given their fixed and random effect specifications, more (or less) closely meet the (binomial logit in your case) specified distribution. Due to the both the approximation and the lack of formal test statistic distribution you would be safer to group the 'best' few together and use some other, even less formal criteria to choose amongst them (or maybe show the main inferences of interest do not materially change amongst the group).
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