[R-sig-ME] REML and LRT

[Viechtbauer Wolfgang (STAT)]

Hello All,

A discussion on r-help got me to think about the following issue.

Suppose we want to conduct a LRT to compare the fit of two nested mixed-effects models differing in their fixed effects. We know that the restricted likelihoods of the two models cannot be directly compared then, so the typical recommendation in the literature is to use ML estimation to fit both models.

However, using REML estimation simply means that the variance components are estimated based on the restricted likelihood (which does not involve any fixed effects) and then plugging the REML estimates of the variance components into the variance-covariance matrix of the observations and using the equation for the ML estimators for the fixed effects (which is just GLS) to estimate those fixed effects.

So, if we look at ML vs REML simply as two different ways of estimating the variance components, then couldn't we simply consider the regular likelihoods of the two models to carry out the LRT even if the variance components have been estimated with REML?

In fact, it was suggested that this is how the anova() function works in lme4. I have not checked this, but I am curious what people think about this issue in general.

Best,

--
Wolfgang Viechtbauer
 Department of Methodology and Statistics
 School for Public Health and Primary Care
 University of Maastricht, The Netherlands
 http://www.wvbauer.com/