YipingÂ Tang, JinfangÂ Wang

We consider model selection problem for linear mixed models. Two types of model selection criteria, the marginal Akaike information criterion (mAIC) and the conditional Akaike information criterion (cAIC) have been used in the literature. However, Greven and Kneib (2010) show that the mAIC is not asymptotically unbiased for the Akaike information, which favours smaller models without random effects. Greven and Kneib (2010) also show that a bias for cAIC also exists if one ignores the estimation uncertainty in the random effect covariance matrix. This bias of cAIC can lead to the selection of any random effect not predicted to be exactly zero. In this paper we apply the bootstrap method to both the marginal log-likelihood functions and the conditional log-likelihood functions to estimate the corresponding marginal Akaike information and the conditional Akaike information. We call the resulting information criteria the marginal extended information criterion (mEIC) and the conditional extended information criterion (cEIC) respectively. The mEIC and cEIC are subject to two types of sampling fluctuations, namely the fluctuation due to original sample and the fluctuation due to bootstrap sampling. Variance reduction method is discussed to reduce the latter bootstrap sampling errors. We demonstrate through simulation studies that mEIC and cEIC perform better than either mAIC or cAIC.

**Keywords:** Linear mixed model; Model selection; Bootstrap; Akaike information

**Biography:** Yiping Tang is a PhD candidate at the Department of Mathematics and Informatics, Chiba University, Japan. He is currently working on modeling selection techniques for linear mixed models using the bootstrap methods. He is also interested in Bayesian statistics and analysis of longitudinal data.