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.
|