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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.

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