Applying negative binomial regression analysis to overcome the overdispersion of Poisson regression model for malnutrition cases in Indonesia

Abstract

Indonesia is one of the developing countries that is struggling to eradicate malnutrition problem. Malnutrition that occurs over a long period of time can have an impact on deaths for the sufferers and decreasing human’s quality of life. This study aims to model the case of malnutrition that occurred in Indonesia Provinces during 2015, and get the main factors that cause malnutrition problem. Variables studied consists of Malnutrition (Y), Vitamin A consumption (X1), Exclusive breastfeeding (X2), Immunization (X3), Water quality (X4), Healthcare center (X5), and Poverty level (X6). Based on the Kolmogorov-Smirnov test, the results of malnutrition data in Indonesia Province in 2015 does not follow Poisson distribution because of overdispersion. The presence of overdispersion cases in the Poisson regression model will have an impact on the inappropriateness of inferences. An alternative model that can accomodate this case is negative binomial regression model.  By using this model, factors that are considered influencing malnutrition cases in Indonesia provinces in 2015 are Immunization (X3), Water quality (X4), and Poverty level (X6). The best model obtained from negative binomial regression analysis is μ ̂_i=exp(2.5111-0.0338X_3+0.0295X_4+0.0576X_6).