統計学輪講（第21回） 日時 2012年11月27日(火) 14時50分～15時40分 場所 経済学部新棟３階第３教室 講演者 川久保友超 (経済M2) 演題 Comparison of Information Criteria for Predictive Variable Selection in Linear Mixed Models 概要 In the problem of selecting the explanatory variables and the random effects in the linear mixed models, we suggest 2 new criteria and compare them with conventional ones: the marginal AIC (mAIC) and the conditional AIC (cAIC). The cAIC can be interpreted as measuring the prediction error of the plug-in predictive density in the context of the Bayesian prediction problem. In this framework, it is known that the Bayesian predictive density improves on the plug-in predictive density. Thus, we suggest the information criterion based on the Bayesian predictive density, which is here called the Bayesian predictive AIC (bpAIC). We also suggest the conditional predictive information criterion (cPIC), which uses the conditional predictive density directly instead of the plug-in predictive density. The penalty (bias correction) terms in these criteria are estimated by Taylor series expansions and paremetric bootstrap methods. Finally, the numerical performance of the proposed information criteria are investigated through simulation studies.