Date of Award

4-2016

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Dr. Rajib Paul

Second Advisor

Dr. Magdalena Niewiadomska-Bugaj

Third Advisor

Dr. Joseph W. McKean

Fourth Advisor

Dr. Kathleen M. Baker

Keywords

Bayesian, variable selection, zero-inflated, negative binomial, spatial, bivariate

Abstract

Count data with excess zeros widely occur in ecology, epidemiology, marketing, and many other disciplines. Mixture distributions consisting of a point mass at zero and a separate discrete distribution are often employed in regression models to account for excessive zero observations in the data. While Poisson models are very popular for count data, Negative Binomial models provide greater flexibility due to their ability to account for overdispersion.

This research focuses on developing a method for analyzing bivariate count data with excess zeros collected over a lattice. A bivariate Zero-Inflated Negative Binomial Hurdle (ZINBH) regression model with spatial random effects is developed. The proposed model characterizes spatial and cross-spatial dependencies. Inferences on model parameters and predictions are done using samples from a Markov Chain Monte Carlo algorithm. We applied our proposed model on Michigan county level crime incidence data. In addition, a method for variable selection through Bayesian penalized regression is developed using a LASSO-type method and elastic net.

Access Setting

Dissertation-Open Access

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