Parameter Estimation and Hypothesis Testing on Bivariate Poisson Log-Normal Regression Models
Fittrofin Amalia Farisa (a*), Purhadi (a), dan Achmad Choiruddin (a)

a) Department of Statistics : Faculty of Science and Data Analysis, Institut Teknologi Sepuluh Nopember, Jl. Arief Rahman Hakim, Surabaya, 60111, Indonesia
*fittrofin[at]gmail.com
purhadi[at]statistika.its.ac.id
choiruddin[at]its.ac.id

Abstract

The aims of this study is to introduce a bivariate Poisson Log-Normal regression model and to develop technique for parameter estimation and hypothesis testing. We term the model Bivariate Poisson Log-Normal Regression (BPLNR). The estimation procedure using an EM algorithm. However, in this case, since the expectations are not easy to obtain we may switch to a Monte Carlo EM approach. To perform hypothesis testing, we adapt the Maximum Likelihood Ratio Test (MLRT) for simultaneous testing with test statistics which, for large n, follows Chi-Square distribution with degrees of freedom p. In addition, the partial testing is derived from a central limit theorem which results in a Z-test statistic.

Keywords: BPLNR, EM, MLRT, Poisson Log-Normal

Topic: MATHEMATICS AND STATISTICS