Selection of covariance structures in GLIMMIX

[SteveDenham]

Stroup and Claassen (2020) recently published an article titled Pseudo-Likelihood or Quadrature? What We Thought We Knew, What We Think We Know, and What We Are Still Trying to Figure Out in the Journal of Agricultural, Biological and Environmental Statistics doi.org/10.1007/s13253-020-00402-6  (paywall, unless you are an ASA member).  In the article, they give some very solid reasoning for using the default RSPL method for GLIMMIX for a variety of distributions.  Now comes the problem - RSPL does not allow for the calculation of information criteria, as the linearization leads to different pseudo-data for various covariance structures.

My question is this - would it make sense to use Gaussian quadrature or Laplace method to select a covariance structure based on (for instance) AICC, and then switch to RSPL for a final analysis?

SteveDenham