Parameter Estimation and Statistical Test in Mixed Model of Geographically Weighted Bivariate Poisson Inverse Gaussian Regression

Poisson regression is nonlinear regression analysis of the Poisson distribution used to analyze discrete data. In Poisson regression requires conditions where the mean and variance values of the response variable are equal or in an equidisperion conditions. However, in many cases over dispersion or under dispersion frequently occurs. One of method to resolve over dispersion and under dispersion cases is the distribution of Poisson Inverse Gaussian (PIG). Not all of the cases in Poisson Inverse Gaussian have only one response variable, in fact some cases will have more than one response variable. In this research, bivariate regression model was developed which involves spatial factor with geographic weighting. In fact, not all variables in the geographically weighted regression model (GWR) have spatial impact, there are several predictor variables has global impact. This research use Maximum Likelihood Estimation (MLE) with Newton-Raphson iteration to obtain parameter model estimator. Afterwards, get the test statistic on the Mixed Geographically Weighted Bivariate Poisson Inverse Gaussian Regression (MGWBPIGR) model using Maximum Likelihood Ratio Test (MLRT).