Comparison between Poisson, Quasi-Poisson, and negative binomial regression in analyzing under-five children malnutrition cases in East Java

Abstract

The most straightforward counted data regression is Poisson regression. The problem often discovered in Poisson regression is overdispersion. Some alternatives regression that can be used in an overdispersed counted data are quasi- Poisson and negative binomial regression. This study will identify the most appropriate and suitable regression in modelling the number of under-five children malnutrition cases in East Java as an overdispersed counted data. The data was obtained from 2018th East Java Health Profile Book. Comparison between Poisson, quasi-Poisson, and negative binomial regression will be made based on a prediction plot, a mean-variance plot, and a comparison plot of observation weight in IWLS algorithm. The comparison shows that quasi-Poisson regression is more suitable for modeling the number of under-five children malnutrition cases in East Java. Hypothesis testing result in 10% significance level shows that the percentage of under-five children who receive exclusive breastfeeding, the percentage of under-five children who receive health services at least 8 times, and the percentage of population with proper sanitation access are factors that significantly affect the number of under-five children malnutrition cases in East Java. Based on the three significant factors, 37 regions in East Java later clustered into three clusters with their characteristics.