Model Selection for the Linear Mixed Model in which the Response is Transformed

• Activity Number: 224
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Matthew J. Gurka*+ and Lloyd J. Edwards and Pranab K. Sen
• Companies: University of North Carolina, Chapel Hill and University of North Carolina, Chapel Hill and University of North Carolina, Chapel Hill
• Keywords: model selection ; linear mixed model ; longitudinal data ; transformations ; AIC ; residual likelihood

Abstract

Shi and Tsai (2002) proposed a residual likelihood criterion (RIC) for univariate linear model selection using a residual likelihood approach to estimation. The selection criterion is based on the expected Kullback-Leibler information of the residual log-likelihood of the fitted model. The Box-Cox transformation was treated as a special case of a generalized version of the univariate linear model. The methodology of the RIC is extended to the linear mixed model for longitudinal data in which the response is transformed using the Box-Cox approach. Consistency properties of the RIC proved theoretically for the univariate case are shown to hold true for the transformed mixed model as well. Extensive simulations are performed to assess the performance of the RIC in selecting the "best" transformed mixed model for both large and small samples. Specifically, the ability of the RIC to select the correct fixed effects structure for a given mixed model with a transformed response in both large and small sample settings is examined, and we compare its performance to those of existing criteria used in the linear mixed model, such as the AIC and BIC.