Fitting of Generalized Poisson Regression and Negative Binomial Regression models for Analyzing of Count Time Series Event

Abstract

Abstract—The focus of this paper is fitting the appropriation of two regression models of discrete count data, Poisson and Negative binomial regression models. The question is which one of these two models is the best choice for predicting the number of (EIA pax aircraft movement from Erbil international Airport) during specific period of time from (2015-2021). To model count data, Poisson regression has been widely used. It is frequently criticized, nevertheless, for the strong requirement of equidispersion in Poisson regression, which entails equality between the variance and mean of the dependent variable. Count data frequently displays excess zeroes and over-dispersion in many applications. While Negative binomial regression can model over-dispersed count data. There are instances of both overdispersion and underdispersion. One technique that can deal with overdispersion and underdispersion is Generalized Poisson regression (GPR). The data set is fitted to the specific models by a method called Maximum Likelihood estimation. This means that the unknown coefficients are estimated such as the likelihood of getting the given data is as large as possible. The dependent variable for the real data was the number of EIA pax aircraft movement weekly with the 13 independent variables. Four criterions used to check over dispersion and goodness of fit like Pearson statistic, Deviance, AIC and BIC as test statistic; these are the common ways of comparing likelihoods between different models with respect to the number of estimated parameters.  Empirical results supported the Negative Binomial Regression Model fitted data set very well depending on the values of these criterions, as their smaller values indicate the best model. modeled dataset by available statistical software like SPSS V25 and Stata V16 and Stratigraphic V15.