Abstract
For model selection in mixed effects models, Vaida and Blan chard (2005) demonstrated that the marginal Akaike information criterion is appropriate as to the questions regarding the population and the conditional Akaike information criterion is appropriate as to the questions regarding the particular clusters in the data. This article shows that the marginal Akaike information criterion is asymptotically equivalent to the leave-one-cluster-out cross-validation and the conditional Akaike information criterion is asymptotically equivalent to the leave-one-observation-out cross-validation.
Highlights
Linear mixed effects models (Laird and Ware, 1982) are powerful for the analysis of clustered data, longitudinal data, meta data analysis, and recently for the functional data analysis (e.g., Brumback and Rice, 1998; Rice and Wu, 2001)
Akaike information criteria (AIC; Akaike, 1973) are most popular, and they are of a similar formula, AIC = −2log likelihood + 2K, where K is the number of effective degrees of freedom measuring the model complexity
Vaida and Blanchard (2005) demonstrated that the marginal Akaike information criterion is appropriate as to the questions regarding the population and the conditional Akaike information criterion is appropriate as to the questions regarding the particular clusters in the data, where in the mAIC the effective degrees of freedom are the number of fixed parameters and in the cAIC the effective degrees of freedom are the ρ proposed by Hodges and Sargent (2001)
Summary
Linear mixed effects models (Laird and Ware, 1982) are powerful for the analysis of clustered data, longitudinal data, meta data analysis, and recently for the functional data analysis (e.g., Brumback and Rice, 1998; Rice and Wu, 2001). The general cAIC developed by Liang et al (2008) coincides with the concept of generalized degrees of freedom developed by Ye (1998) This finding clearly classifies the AIC criteria for mixed effects models existing in the literature into two main streams, the mAIC and the cAIC. After establishing the asymptotic equivalences between the CLCV and the mAIC and between the OBCV and the cAIC, I can conclude that the CLCV is appropriate as to the questions regarding the population and the OBCV is appropriate as to the questions regarding the particular clusters in the data This conclusion applies to other model selection problems, such as bases selection in functional data analysis, and bandwidth selection in the local polynomial mixed effects models
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