Model Selection in Mixed Effects Models Based on the Relative Quadratic Risk

• Activity Number: 656
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Rositsa Dimova* and Marianthi Markatou
• Companies: SUNY Buffalo and SUNY Buffalo
• Keywords: Model Selection ; Quadratic Distances ; Mixed Effects Models ; QIC

Abstract

The most commonly used approaches for model selection in mixed effects models are the AIC, its finite sample version AICc and BIC. AIC and its variants rely on the Kullback-Leibler distance as a loss function, while BIC relies on the use of the likelihood. Here, we present an alternative method for model selection in mixed effects models, the Quadratic Information Criterion (QIC), derived as an estimator of the relative quadratic risk. The latter is based on a quadratic distance (Lindsay et al. (2008, 2013)) between the true distribution of the data and the approximating distribution of interest. An appealing feature of the quadratic distances between distributions is that many distances (incl. the Kullback-Leibler) can be approximated by them. Furthermore, the option for a choice of a kernel function and a tuning parameter makes quadratic distances, and hence the criteria based on them, very flexible and adjustable to the distributions of interest. Subsequently, we investigate the performance of the proposed criterion for different tuning parameters and compare it to that of AIC type and BIC criteria.