Parameter Estimation and Hypothesis Testing of Geographically Weighted Bivariate Zero Inflated Poisson Inverse Gaussian Regression Models

Abstract

Count data is data that can be counted within a certain range of time. The count data itself can be accommodated in the Poisson distribution which is always positive value. Poisson regression is often used to model count data, but Poisson regression requires equality in means and variance (equidispersion). The count data often contains many zero values and is unable to meet the equidipersion assumption. Zero Inflated Poisson Inverse Gaussian Regression (ZIPIGR) is a mix poisson regression that can accommodate under/overdispersion and also the number of zero values in the data. ZIPIGR is global regression model, so the interpretation of the model obtained is global in all observational data. The ZIPIGR method that accommodate the location factor is the Geographically Weighted ZIPIGR (GWZIPIGR). Bivariate GWZIPIGR (GWBZIPIGR) can be used when there are two response variables that correlate each other. This paper will discuss parameter estimation of GWBZIPIGR using Maximum Likelihood Estimation (MLE) and numerical iteration of Berndt Hall Hall Hausman (BHHH) is used when the result of estimation equation does not close form, Meanwhile Maximum Likelihood Ratio Test (MLRT) is used to test the parameters where simultaneous hypothesis testing used the G2 test statistic at large sample with X2 distribution.