First Advisor

Schaffer, Jay Ryan, 1969-

Second Advisor

Lalonde, Trent L.

Document Type

Dissertation

Date Created

8-1-2013

Department

College of Education and Behavioral Sciences, Applied Statistics and Research Methods, ASRM Student Work

Abstract

Count data regression models are used for special cases where the response variable takes count values or only non-negative values. Poisson regression models are commonly used to analyze count data. A frequent problem with the use of these models is that the observed variation is greater than expected and mixed Poisson models are alternative models that provide a means of explaining the extra-Poisson variation. Mixed Poisson regression models have extensive research and literature studies, and have been commonly used in fields such as epidemiology, medicine, genetics, economics, engineering, marketing, and in the physical and social sciences. However, in many cases, the analyst does not observe the entire distribution of counts. In such a case, the count data are truncated as the data are observed only over part of the range of the response variable. In this study, we formulate a class of regression models based on a Double Truncated Poisson regression model with random effects. Two different distributions for the random effects, Normal and Gamma, were studied through simulation. Misspecification of these distributions was addressed. Comparisons with the Left Truncated Mixed Poisson model and the regular Mixed Poisson model were presented. It was concluded that with Normal random effects, double and Left Truncated Mixed Poisson models provide a better fit to clustered double truncated count data compared to the regular mixed Poisson model. For Gamma random effects, the Double Truncated Mixed Poisson model provides a better fit to clustered double truncated count data. These models were used to analyze a Transitional Housing Facility data set.

Abstract Format

html

Keywords

Poisson's equation -- Numerical solutions; Random fields; Multivariate analysis; Statistics

Extent

187 pages

Local Identifiers

Suaiee_unco_0161D_10234

Rights Statement

Copyright is held by author.

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