Hypothesis testing of Geographically weighted bivariate logistic regression

Abstract

In this study, the hypothesis testing of geographically weighted bivariate logistic regression (GWBLR) procedure is proposed. The GWBLR model is a bivariate logistic regression (BLR) model which all of the regression parameters depend on the geographical location in the study area. The geographical location is expressed as a point coordinate in two-dimensional geographic space (longitude and latitude). The response variables of BLR model are constructed from a (2 × 2) contingency table and it follows the multinomial distribution. The purpose of this study is to test the GWBLR model parameters. There are three hypothesis tests. The first is a parameters similarity test using the Vuong test method. The test is to obtain a significant difference between GWBLR and BLR. The second is a simultaneous test using the likelihood ratio test method. The simultaneous test is to obtain the simultaneous significance of the regression parameters. The last is a partial test using Wald test method. The result showed that the Vuong statistic and Wald statistic have an asymptotic standard normal distribution, whereas the likelihood ratio statistic has an asymptotic chi-squared distribution.