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UBC Theses and Dissertations

Modeling zero inflated count data Garden, Cheryl Ellen


A natural approach to analyzing the effect of covariates on a count response variable is to use a Poisson regression model. A complication is that the counts are often more variable than can be explained by a Poisson model. This problem, referred to as overdispersion, has received a great deal of attention in recent literature and a number of variations on the Poisson regression model have been developed. As such, statistical consultants are faced with the difficult task of identifying which of these alternative models is best suited to their particular application. In this thesis, two applications where the data exhibit overdispersion are investigated. In the first application, two treatments for chronic urinary tract infections are compared. The response variable represents the number of resistant strains of bacteria cultured from rectal swabs. In the second application, the number of units sold of a product are modeled as depending on two factors representing the day of the week and the store. Two alternative models that allow for overdispersion are used in both applications. The negative binomial regression model and the zero inflated Poisson regression model so named by Lambert (Lambert, 1992) provide improved fits. Further, the zero inflated Poisson regression model performs particularly well in the situation when the overdispersion is suspected to be due to a large number of zeroes occurring in the data. The zero inflated Poisson regression model allows one to both fit the data well and make some inference regarding the nature of the overdispersion present. This little known model may prove to be valuable as there exist a number of applications where observed overdispersion in a count response variable is clearly due to an inflated number of zeroes.

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