Hypothesis testing of geographically weighted multivariate poisson regression

Geographically weighted multivariate Poisson regression (GWMPR) model is a local form of the multivariate Poisson regression (MPR) that allows the modelling of spatially heterogeneous processes. This model results in a set of local parameter estimates which depends on the geographical location where the data are observed. In this paper, hypothesis testing in GWMPR model is studied which includes a goodness of fit test, an overall test and test of individual parameters. The test statistic of all the three hypotheses testing of the GWMPR model is done by using likelihood ratio test (LRT) method. The test statistic of the goodness of fit test follows the asymptotic distribution of chi-square with the degree of freedom is the difference between the effective number of parameters in the MPR and GWMPR models. The second test statistic of the overall test follows the asymptotic distribution of chi-square with the degree of freedom is the difference between the effective number of parameters in the GWMPR without the covariate in the model and GWMPR model whereas the test statistic of the test of individual parameters follows the asymptotic distribution of the standard normal.