Are there any conventions for the use of bias correction methods in G-side generalized linear mixed models (GLMMs)?
For linear mixed models I usually use the Kenward and Roger adjustment, but it is undefined for G-side GLMMs.
My data is from a 2 x 3 factorial design with repeated measures in a randomized complete block. The response variable is binomial and I'm using a logit link. I'm using integral approximation (I've tried Laplace and quadrature) instead of PL because I want to compare fit statistics for different covariance structures, but I think I've settled on a heterogeneous autoregressive structure.
The problem is that I get different model results depending on the correction that I use. So far I have implemented the model 3 ways:
- Uncorrected estimates
- Sandwich (Empirical/Classical) estimators
- Sandwich estimators with Morel et al. adjustment
The F tests have different results depending on the method ... The Morel correction seems to be incredibly conservative, the empirical sandwich estimators are quite liberal and the uncorrected estimates are somewhere in the middle.
I am currently using the GLIMMIX procedure in SAS but I intend to repeat the analysis in R.
Which results do I report? I'm new to GLMMs but I've read that some correction method should be implemented to account for the downward bias associated with the estimating the fixed effects after accounting for the random effects.