Overdispersion Handling in Poisson Regression Model by Applying Negative Binomial Regression

Abstract

Statistical analysis that can be used if the response variable is quantified data is Poisson regression, assuming that the assumption must be met equidispersion, where the average response variable is the same as the standard deviation value. A negative binomial regression can overcome an unfulfilled equidispersion assumption where the mean is greater than the standard deviation value (overdispersion). This method is more flexible because it does not require that the variance be equal to the mean. The case studies used in this research are cases of anemia in women of childbearing age (WCA) in 33 provinces of Indonesia. This study aims to apply the Poisson regression method and negative binomial in the case data of anemia in WCA to prove the model's goodness and find the factors that influence anemia in WCA. This data was obtained from biomedical sample data for Riset Kesehatan Dasar (Riskesdas) and data obtained from the website of the Badan Pusat Statistik (BPS) in 2013. By applying these two methods, the result is that negative binomial regression is the best model in modeling WCA cases with anemia in Indonesia because it has the smallest AIC value of 221.72; however, the difference is not too far from the AIC in the Poisson regression model, which is 221.83. It can also be supported that Poisson regression is unsuitable for the analysis because of the case of overdispersion. With a significance level of 10%, the number of WCA affected by malaria per 100 population influences cases of WCA anemia. At the same time, other independent variables have no effect.