Section: New Results

A new Bayesian Information Criteria for mixed-effects models

Participants : Maud Delattre, Marie-Anne Poursat, Marc Lavielle.

The Bayesian Information Criterion (BIC) is widely used for variable selection in mixed effects models. However, its expression is unclear in typical situations of mixed effects models, where simple definition of the sample size is not meaningful. Yet, in the mixed effects model literature, the BIC penalty usually involves the total number of observations $log{n}_{\mathrm{tot}}$. From a practical point of view, the $log{n}_{\mathrm{tot}}$ penalty is implemented in the R package nlme and in the SPSS procedure MIXED while the $logN$ penalty, where $N$ is the number of subjects, is used in MONOLIX, saemix or in the SAS proc NLMIXED.

We have derived an appropriate BIC expression that is consistent with the random effect structure of the mixed effects model [7] . We have illustrated the behavior of the proposed criterion through a simulation study. The use of this new version of BIC is recommended as an alternative to various existing BIC versions that are implemented in available software.