Assessing Adequacy of the Covariance Structure in the Generalized Linear Mixed Model

• Activity Number: 385
• Type: Contributed
• Date/Time: Wednesday, August 11, 2004 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Jean Orelien*+
• Companies: SciMetrika
• Keywords: mixed model ; goodness-of-fit ; covariance structure

Abstract

In the generalized linear mixed model, few tools are available for assessing the adequacy of the covariance structure. Statistics such as the Likelihood Ratio Test (LRT), the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC) provide a way to compare the fit of a model against another one. Other statistics such as the concordance correlation coefficient and other pseudo R-squares have been proposed to assess goodness-of-fit for the model at hand without requiring the fit of a second model. None of the statistics mentioned above provide a way to ascertain the appropriateness of the covariance structure. Vonesh and Chinchilli (1986) proposed a test to compare the covariance of the parameter estimates from a generalized linear mixed model to the robust covariance matrix from a generalized estimated equation (GEE) model. However, the performance of this test has not been fully evaluated in simulation (results from a limited simulation of 400 samples were offered) or proven analytically. We present results from a simulation that estimates the empirical Type I error rate and power of this test for various types of covariance structures.