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Frequentist approaches to overdispersed repeated measures count data
Repeated measures data refers to data sets in which observations are taken on each subject at multiple time points over a period of interest. In contrast to the analysis of independent data, repeated measures analysis must account for dependencies between observations on the same subject. With respect to count data, the term overdispersed refers to data that violates the mean-variance equality of a Poisson distribution. While the analysis of data exhibiting either one of these two properties has been described extensively, methods for analyzing data exhibiting both properties are less well-understood. The archetypal data set exhibiting these two properties is the so-called "seizure data set." Many approaches to analyzing these data appear in the literature. The classes of models suggested range from fully parametric conditional models to semi-parametric marginal (or GEE-type) models. The natural question is: "which, if any, of these methods should we use?" Outside asymptotic theory, answering this question requires simulated data. Thus, study of the processes that plausibly give rise to such data is a crucial first step. Probability processes for repeated measures data can generally be classified as observation driven or latent process approaches. Because probability processes for overdispersed count data inherently involve latent variables, the latter is more amenable to producing overdispersed repeated measures count data. Latent processes for producing overdispersed count data include Poisson processes conditioned on multivariate Gaussian variables and Poisson processes conditioned on multivariate gamma variables. The advantage of utilizing the former is the wide variety of multivariate Gaussian distributions available, while use of the latter aligns with methodology for producing independent, overdispersed count data. This thesis expands on multivariate gamma distributions, and examines the use of these distributions for producing overdispersed repeated measures count data. Characterization of the probability processes provides a basis for simulating overdispersed repeated measures count data. The relative merits of each class of models are explored via a simulation studying comparing their small-sample behavior under each of the previously described probability processes.
Frenzel, Martin J, "Frequentist approaches to overdispersed repeated measures count data" (2012). ETD collection for University of Nebraska - Lincoln. AAI3518912.