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I would like to make an enquiry regarding the use of ML or REML for GLMM. At the moment, I'm focusing on doing model selection to evaluate the effect of four fixed effects and one random effect on a response variable (continuous data) in a study of behavioural ecology. My global model is close to a Gaussian distribution after log-transformation, but does not completely satisfy the assumption of normality of residuals. Therefore, I'm using GLMM (family = Gaussian) rather than LMM.

My question is: should I use ML or REML as a method of model fitting? I'm quite new to R and model selection, but from what I have read in several books (e.g., Generalized, Linear and Mixed Models, by McCulloch and Searle), I understand that REML should only be used to select random effects for a constant set of fixed effects, so I'm inclined to use ML for model estimation. I'm not 100% sure if that's the right thing to do. The default in LMM is set to REML = TRUE, but I'm not sure what is the best method of estimation for GLMM.

jonsca
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user20347
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    A couple of points (maybe not quite worthy of an answer, so I'll make it a comment for now): (1) as far as I know, GLMM with a Gaussian family is a standard LMM, unless you use a non-standard (i.e. non-identity) link; (2) REML is not commonly implemented for GLMMs (and in particular not in lme4); I guess you can use it with glmmPQL from the R MASS package. If it is implemented, I would say that the rules for ML vs REML are more or less the same as those for LMMs (i.e. don't compare REML fits with different fixed effects) – Ben Bolker Mar 10 '13 at 17:34

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