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Generalized linear mixed models have played an important role in the analysis of longitudinal data; however, traditional approaches have limited flexibility in accommodating skewness and complex correlation structures. In addition, the existing estimation approaches generally rely heavily on the specifications of random effects distributions; therefore, the corresponding inferences are sometimes sensitive to the choice of random effect distributions under certain circumstance. In this paper, we incorporate serially dependent distribution-free random effects into Tweedie generalized linear models to accommodate a wide range of skewness and covariance structures for discrete and continuous longitudinal data. An optimal estimation of our model has been developed using the orthodox best linear unbiased predictors of random effects. Our approach unifies population-averaged and subject-specific inferences. Our method is illustrated through the analyses of patient-controlled analgesia data and Framingham cholesterol data. [ABSTRACT FROM AUTHOR]

In medical and health studies, heterogeneities in clustered count data have been traditionally modeled by positive random effects in Poisson mixed models; however, excessive zeros often occur in clustered medical and health count data. In this paper, we consider a three-level random effects zero-inflated Poisson model for health-care utilization data where data are clustered by both subjects and families. To accommodate zero and positive components in the count response compatibly, we model the subject level random effects by a compound Poisson distribution. Our model displays a variance components decomposition which clearly reflects the hierarchical structure of clustered data. A quasi-likelihood approach has been developed in the estimation of our model. We illustrate the method with analysis of the health-care utilization data. The performance of our method is also evaluated through simulation studies. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]