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.
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
Multivariate Zero-Inflated Poisson Regression.
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