Parameter estimation of geographically weigthed multivariate poisson regression

Geographically Weighted Multivariate Poisson Regression (GWMPR) is a statistical technique on spatial data which is used to modelling of relationships between two or more response variables (Poisson distribution) and one or more independent variables. The underlying idea of GWMPR model is that for each estimator of the regression parameters depend on the location where the data are observed. The locations is expressed as a point coordinate in two-dimensional geographic space (latitude and longitude). In this paper is studied the problem of parameters estimation in GWMPR model by using Maximum Likelihood Estimation ( MLE ) method. This method cannot find an analytical solution since the first derivatives of the log-likelihood function is not available in closed form. Therefore, in this study we apply iterative procedure by the Newton-Raphson algorithm. Finally, an empirical study is carried out to demonstrate the performance of the parameter estimation of GWMPR models, where each model will be analyzed for covariance as constant and cavariance as a function of the independent variables.