Negative Binomial Regression Analysis on Dengue Hemorrhagic Fever Cases in East Kalimantan Province

Abstract

Poisson regression is commonly used in modeling count data. An essential assumption of the Poisson regression model is that the mean of the response variable is equal to the variance, namely equidispersion. Many fields of research were the data overdispersed, which is the variance greater than its mean. Therefore, the Poisson regression model is not suitable to model it. The negative binomial regression (NBR) model is a solution of the Poisson regression model when the response variable is an overdispersion count data. This study aims to build an NBR model and apply it to model the dengue hemorrhagic fever (DHF) cases in East Kalimantan Province, Indonesia, in 2019. The maximum likelihood estimation and Fisher scoring methods were used to estimate the NBR model parameters, whereas the significant test containing the overall and individual tests was done using the likelihood ratio and Wald test statistics. Based on data analysis, the mean and variance values of the DHF data in East Kalimantan Province were 672 and 386113, respectively, and it shows that the DHF cases in East Kalimantan Province, Indonesia, in 2019 were an overdispersed count data. The factors that affected the DHF cases in East Kalimantan Province, Indonesia, in 2019 based on the NBR model were the total area, the area altitude, population density, and the health workers.