I am using Mixed effects models (
nlme package in R) to choose the model with the best random and fixed effects. I am following the procedure of Zurr et al. (2009) and read about "testing on the boundary" and the effects that it has on p values. From what I have read, it looks as though this is only something that is a problem when using REML, but I am not sure.
My questions are:
When performing a LRT between 2 nested models which only differ in fixed effects (thus using ML instead of REML), do the p values have to be adjusted for testing on the boundary?
If this is a problem only for REML estimation, why? Does it have to do with the REML estimation itself, or the fact that it is usually used with the LRT when comparing models that differ in random effects?