Modified BIC Criterion for Model Selection in Linear Mixed Models

Linear mixed-effects models are widely used in applications to analyze clustered, hierarchical, and longitudinal data. Model selection in linear mixed models is more challenging than that of linear models as the parameter vector in a linear mixed model includes both fixed effects and variance component parameters. When selecting the variance components of the random effects, the variance of the random effects must be non-negative and the parameters may lie on the boundary of the parameter space. Therefore, classical model selection methods cannot be directly used to handle this situation. In this article, we propose a modified BIC for model selection with linear mixed-effects models that can solve the case when the variance components are on the boundary of the parameter space. Through the simulation results, we found that the modified BIC performed better than the regular BIC in most cases for linear mixed models. The modified BIC was also applied to a real dataset to choose the most-appropriate model.