Parameter Estimation and Hypothesis Testing of Geographically and Temporally Weighted Bivariate Negative Binomial Regression

Abstract

When the response variable is discrete as a number (count) and there is a violation of the assumption of equidispersion, namely overdispersion or underdispersion then one of the appropriate alternative models used is Negative Binomial Regression (NBR). Moreover, if there are two correlated response variables and have an equidispersion violation, the Bivariate Negative Binomial Regression (BNBR) model is the solution. However, the BNBR model is considered inappropriate if the data contains spatial and temporal heterogeneity derived from panel data with the unit of observation in the form of a region. Therefore, a model is offered which is known as Geographically and Temporally Weighted Bivariate Negative Binomial Regression (GTWBNBR) which accommodates spatial and temporal effects. This study aims to conduct parameter estimates and test statistics for the GTWBNBR model. Estimated parameters use Maximum Likelihood Estimation (MLE) with BHHH numerical iteration because the MLE estimates are not closed-form. When the sample size is large, the Maximum Likelihood Ratio Test (MLRT) is used for simultaneous parameter testing while the test statistic for partial parameter testing approaches the Chi-Square distribution so that it can be tested using the Z-Test. Keywords: parameter estimation, hypothesis testing, GTWBNBR