Goodness-of-Fit Tests in Generalized Linear Mixed Models

• Activity Number: 170
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Min Tang*+ and Eric V. Slud and Ruth Pfeiffer
• Companies: University of Maryland and University of Maryland and National Cancer Institute
• Keywords: Generalized Linear Mixed Model ; Goodness of Fit Test ; longitudinal studies

Abstract

GLMMs are widely used in many fields including biomedical research. The random effects allow one to accommodate correlations due to repeated measures on the same individual, such as in longitudinal studies or due to familial correlations that are seen in family studies in genetic epidemiology. We propose a class of omnibus chi-squared goodness of fit tests for GLMMs that jointly assesses the appropriateness of the measured covariates in the model and the latent random effect. The test statistics are quadratic forms in the observed minus expected differences in cells defined by covariates. We show that under mild conditions, these test statistics have asymptotic chi-square distributions. We apply these tests to models of longitudinal serum measurements taken on women who participated in an alcohol feeding study.