# Likelihood ratio tests using ML vs. REML

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:

1. 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?

2. 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?

• It's hard to say w/o more information. I suspect you are confusing testing FEs vs REs. Can you quote more of the text here? – gung - Reinstate Monica Mar 27 '15 at 22:07
• The text warning about boundary effects is in a section about choosing the best RE structure in your model by comparing models that differ in their RE structure (ie. same FE). When mentioning using the Likelyhood ratio test to test between two models with different RE structures, Zuur warns about boundary effects and that p-values have to be adjusted. He also suggests that REML be used instead of Max Likelyhood to find the optimal random structure for a model, so I was curious if boundary effects were a property of choosing REML estimation, or because we are testing between random effects. – MANOVAboard Mar 31 '15 at 21:27