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Abstract
Zero- Inflated (ZI) regression models are used to account for" excess" zeros in data. Examples include ZI-Poisson, ZI-Binomial models and so on. Recently, extensions of these models to ZI clustered data case have begun to appear. For example, random effects are introduced into the model to take correlations into account within each cluster. In this dissertation, we introduce an alternative approach to fit ZI clustered data based on the Expectation-Solution (ES) algorithm incorporating generalized estimating equations (GEEs). The ES algorithm is a generalization of the Expectation- Maximization (EM) algorithm hy substituting the maximization step with a solution step. We illustrate this method by applying it to fit the whitefly data from van Iersel, Oetting and Hall (2000), and some data concerning apple tree root propogation from Marin, Jones and Hadlow (1993). To apply our new methodology (ES-GEE), we need to select an appropriate working correlation structure for the model. Therefore, we derive a model selection criterion which can he used in selecting both correlation structure and covariates for ZI regression models in the ES-GEE context. This criterion is a modified version of Akaike's Information Criterion (AIC) based on replacing the loglikelihood with the quasilikelihood function. The performance of the criterion is examined through simulation studies. For illustration, we apply this model selection criterion to a real data set. ZT regression models are special cases of generalized finite mixture models with two components. Thus, we extend our model selection criterion from ZT models to generalized mixture model context. Again, its performance is investigated hy simulation studies.