There are many ways to construct a covariance matrix for subjects with a single repeated measurement factor, and there are very many more ways when there are two repeated measures factors. In the MIXED procedure, we have access to Kronecker products (UN@UN, UN@AR(1), and UN@CS), but these options don't exist for GLIMMIX. And there could be more parsimonious covariance matrices than those using UN. I would think that logic and context could help determine plausible structures--what might be correlated and in what fashion.   You might find this paper by Tao, Kiernan and Gibbs (2015) to be helpful:   http://support.sas.com/resources/papers/proceedings15/SAS1919-2015.pdf   I dinked around with various constructions awhile back. I'll attach my code. I won't guarantee that the code (or the descriptions within) are correct, it really ought to be thought of as a work in progress. But perhaps it will be of some use.    As far as your modeling protocol goes, once you settle on a covariance structure, then you could base model selection on AIC (because Laplace is a maximum likelihood method). But I wouldn't; I usually use the approximate tests provided by GLIMMIX, using ddfm=kr, provided the model converges and estimation is decent. For an R-world opinion, see "What is the best way to test hypotheses on effects in GLMMs?" at   http://glmm.wikidot.com/faq   Hope this helps.     ... View more