Date of Award

12-2015

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Dr. Joshua D. Naranjo

Second Advisor

Dr. Joseph McKean

Third Advisor

Dr. Jung Chao Wang

Fourth Advisor

Dr. Mathew Rosales

Keywords

Poisson regression, count data, variance greater than mean, negative binomial regression, overdispersion, equidispersion

Abstract

Commonly used tests for treatment effect in kx2 frequency data are Poisson regression, negative binomial regression, and Cochran-Mantel-Haentzel. In practice, Poisson regression or CMH is used as default, and NB regression is used only when there is reason to believe the data has overdispersion beyond what is expected of Poisson counts.

We show that the Poisson regression is sensitive to the Poisson assumption, and does not maintain its size in the presence of overdispersion. In particular, it tends to interpret overdispersion as significant treatment effect. Thus there is a need for a reliable pretest for the Poisson assumption. A commonly used diagnostic for overdispersion is a Wald test of the estimated overdispersion parameter, however this has convergence problems. We propose a simpler Hogg-type diagnostic that has no convergence problems and is easy to compute.

Access Setting

Dissertation-Campus Only

Restricted to Campus until

12-15-2025

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