Parameter Estimation of Mixed Geographically Weighted Bivariate Zero-Inflated Negative Binomial Regression Model

Abstract

The Bivariate Zero-Inflated Negative Binomial (BZINBR) regression model is commonly used to analyze two correlated count response variables characterized by overdispersion and excess zeros. To account for spatial heterogeneity in predictor effects, the BZINBR model has been extended into the Geographically Weighted BZINBR (GWBZINBR) model. However, predictor effects are not always entirely local; certain global effects may persist across regions. This study proposes the Mixed Geographically Weighted BZINBR (MGWBZINBR) model, which integrates both global and local parameter structures for modeling spatially correlated bivariate count data. The theoretical framework of the MGWBZINBR model is developed, including the derivation of the log-likelihood function, parameter estimation procedures, and hypothesis testing. Parameter estimation is conducted using the Maximum Likelihood Estimation (MLE) method via the iterative Berndt–Hall–Hall–Hausman (BHHH) algorithm. Given the complexity of the likelihood equations and the absence of closed-form solutions, numerical optimization is employed to ensure convergence and stability. The MGWBZINBR model offers a flexible and robust framework for analyzing spatial count data with excess zeros and complex dependency structures. It can be applied in various fields, including public health, ecology, and transportation analysis, to understand the influence of both local and global predictors on spatial phenomena. As the focus of this paper is methodological, empirical and simulation-based applications are intentionally excluded.