Extension of generalized Poisson log-linear regression models for analysing three-way contingency table: Application to malaria data

Abstract

Abstract This study presents the extension of generalized Poisson (GP-1 and GP-2) models for three-way contingency table. We assume a mixed systematic component of the log-linear models for contingency tables to produce a linear transformation for the link function of Generalized Linear Models (GLMs). Maximum likelihood estimation method was derived for the parameters estimates of the models. An over-dispersed malaria data of 2019 was considered for the study. The GP-1 and GP-2 models for three-way contingency table was used to model the data. Based on Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) goodness-of-fits measures, the GP-2 model outperformed the GP-1 model for three-way contingency table on malaria data. We found that some parameters of the full model were statistically significant as; malaria cases was sensitive to all ages considered in the study, and people were more infected with malaria in the month of April, June, and July 2019.