2010 Volume 40 Issue 1 Pages 111-131
The paper addresses the problem of selecting variables in linear mixed models (LMM)νll. We propose the Empirical Bayes Information Criterion (EBIC) using a partial prior information on the parameters of interest. Specifically EBIC incorporates a non-subjective prior distribution on regression coefficients with an unknown hyper-parameter, but it is free from the setup of a prior information on the nuisance parameters like variance components. It is shown that EBIC not only has the nice asymptotic property of consistency as a variable selection, but also performs better in small and large sample sizes than the conventional methods like AIC, conditional AIC and BIC in light of selecting true variables.