What are the best strategies to select between a small collection of possible models when the models are non-nested and modeled using a GLMM with correlated residuals (longitudinal random effects or $R$-side random effects)?

Information criteria comparisons aren't comparable for for different GLMMs due to different pseudo-data.

My only thought was to graphically compare model diagnostics and choose the model that best fits the assumptions. If models were generally comparable, I'd consider the most parsimonious model to be the best candidate. However, I was looking for more statistical methods to compare these kinds of models.

I use both R and SAS, so a connection to either of those would be helpful.

  • $\begingroup$ Cross-validation? $\endgroup$ – Matthew Drury Jun 14 '17 at 1:21
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    $\begingroup$ What do you mean by "different pseudo-data"? AIC can be used for non-nested models if you evaluate them on the same data. $\endgroup$ – Tim Jun 14 '17 at 13:35
  • $\begingroup$ @Tim By pseudo-data, I mean the linearized response variable in the GLMM. SAS documentation states to not compare pseudo-AIC from models (even nested): support.sas.com/documentation/cdl/en/statug/63347/HTML/default/… $\endgroup$ – Ashe Jun 14 '17 at 14:02
  • $\begingroup$ So do you ask about GLM or GLMM? And about AIC or pseudo-AIC ? $\endgroup$ – Tim Jun 14 '17 at 14:03
  • $\begingroup$ I tried to make my question a bit more general by starting with the GLM then asking about the GLMM. My core issue is with the GLMM though. $\endgroup$ – Ashe Jun 14 '17 at 14:04

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