Wang, Yang2017-07-252017-07-252017-06https://hdl.handle.net/11299/189101A 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, tablesIn 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.enPoisson regressionMultivariate distributionMultivariate zero-inflated distributionMaximum likelihood estimatesNewton-Raphson (NR) iterationExpectation-maximization (EM) algorithmSwenson College of Science and EngineeringDepartment of Mathematics and StatisticsMaster of ScienceUniversity of Minnesota DuluthMaster of Science in Applied and Computational MathematicsPlan Bs (project-based master's degrees)Scholarly Text or Essay