Multivariate Zero-Inflated Poisson Regression

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Multivariate Zero-Inflated Poisson Regression

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Wang, Yang

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2017-06

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Abstract

In this report, we develop a procedure to analyze the relationship between the ob- served multi-dimensional counts and a set of explanatory variables. The counts follow a multivariate Poisson distribution or a multivariate zero-inflated Poisson distribution. Maximum likelihood estimates (MLE) for the model parameters are obtained by the Newton-Raphson (NR) iteration and the expectation-maximization (EM) algorithm, respectively. In Newton-Raphson method, the first and second derivatives of the log- likelihood function are derived to carry out the numerical evaluation. Formulas using EM algorithm are also introduced. A comparison of the estimation performance is made from simulation studies.

Keywords

Poisson regression

Multivariate distribution

Multivariate zero-inflated distribution

Maximum likelihood estimates

Newton-Raphson (NR) iteration

Expectation-maximization (EM) algorithm

Swenson College of Science and Engineering

Department of Mathematics and Statistics

Master of Science

University of Minnesota Duluth

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A project submitted to the faculty of the graduate school of the University of Minnesota in partial fulfillment of the requirements for the degree of Master of Science. June 2017. Major: Mathematics and Statistics. Advisor: Yang Li. 1 computer file (PDF); vii, 32 pages, tables

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Master's Degree Culminating Works
Master of Science in Mathematical Sciences and Master of Science in Applied and Computational Mathematics Plan B Project Papers

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Wang, Yang. (2017). Multivariate Zero-Inflated Poisson Regression. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/189101.

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