Multivariate generalized Poisson regression model with exposure and correlation as a function of covariates: Parameter estimation and hypothesis testing

Abstract

This paper presents the parameter estimation and the simultaneous testing for the parameters of a modified multivariate generalized Poisson regression (MGPR) model that takes into account a measure of exposure and defines the correlation as a function of covariates. An exposure is included in the model to account for population size difference of the analysis units in the study where the exposure is not necessarily the same for each response variable. The correlations between the response variable are defined as a function of the covariates with the assumption that each response variable and their correlations are affected by the same covariates. The Newton method with BHHH algorithm is used to obtain maximum likelihood estimators of the modified MGPR model. The test statistic G2 for simultaneous hypothesis testing is achieved using the likelihood ratio method which is asymptotically chi-square distributed with v degrees of freedom.