Information methods for model selection in linear mixed effects models with application to HCV data

In this paper, we derive a small sample Akaike information criterion, based on the maximized loglikelihood, and a small sample information criterion based on the maximized restricted loglikelihood in the linear mixed effects model when the covariance matrix of the random effects is known. Small sample corrected information criteria are proposed for a special case of linear mixed effects models, the balanced random-coefficient model, without assuming the random coefficients covariance matrix to be known. A simulation study comparing the derived criteria and several others for model selection in the linear mixed effects models is presented. We illustrate the behavior of the studied information criteria on real data from a study of subjects coinfected with HIV and Hepatitis C virus. Robustness of the criteria, in terms of the error distributed as a mixture of normal distributions, is also studied. Special attention is given to the behavior of the conditional AIC by Vaida and Blanchard (2005). Among the studied criteria, GIC performs best, while cAIC exhibits poor performance. Because of its inferior performance, as demonstrated in this work, we do not recommend its use for model selection in linear mixed effects models.