"Consistency of the Empirical Bayes Information Criterion for Selecting Variables in Linear Mixed Models"

The paper addresses the problem of selecting variables in the two-stage sampling models characterized as a linear mixed model. We obtain the Empirical Bayes Information Criterion (EBIC) using a prior distribution on regression coefficients with an unknown hyper-parameter. It is shown that EBIC not only has the nice asymptotic property of the consistency as a variable selection, but also performs better in small sample sizes than the conventional methods like BIC and AIC in light of selecting the true variables.