Modified BIC for Model Selection in Linear Mixed Models

Linear mixed effects models are widely used in applications to analyze clustered 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 components parameters. When selecting the variance components of the random effects, the variance of the random effects must be non-negative and therefore, parameters may lie on the boundary of the parameter space. In this dissertation, 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. We first derive a modified BIC to choose random effects assuming that the random effects are independent. Then, we propose a modified BIC to choose random effects when random effects are assumed to be correlated. Lastly, we propose a modified BIC to choose both fixed effects and random effects simultaneously. Through the simulation results, we found that the modified BIC performs well and performs better than the regular BIC in most cases. The modified BIC is also applied to a real data set to choose the most appropriate linear mixed model.