Track: Modeling and Simulation

Abstract

Many phenomena do not follow a symmetrical distribution. In order to obtain accurate conclusions, the analysis used for this phenomenon can be adjusted to the nature of the data distribution that is not symmetrical, for example the gamma distribution. The gamma distribution can be extended into a regression model. The gamma regression relates a positive response variable following a gamma distribution to one or more predictor variables. In this study, we explore a gamma regression with the gamma distribution has three parameters. This paper also presents the parameter estimation, test statistics, and hypothesis testing for the significance of the parameter. The method used for parameter estimation is Maximum Likelihood Estimation (MLE), which is optimized using numerical iteration, namely Berndt-Hall-Hall-Hausman (BHHH) algorithm. Maximum Likelihood Ratio Test (MLRT) is used for simultaneous test, whereas the Wald test is used for partial test. The developed gamma regression model is applied to the education index with three predictor variables, among others, the percentage of households to private toilet ownership, population density, and the percentage of poor people. The unit of observation is regency/city in Java, Indonesia, of the year 2018. The results show that modeling using multiple predictors is better in terms of accuracy of prediction as well as the interpretation. The future work of this research is how to involve geographical factors as a spatial effect in the model.