Geographically Weighted Zero-Inflated Negative Binomial Regression: A general case for count data

Abstract

Poisson and Negative Binomial Regression Models are often used to describe the relationship between a count dependent variable and a set of independent variables. However, these models fail to analyze data with an excess of zeros, being Zero-Inflated Poisson (ZIP) and Zero-Inflated Negative Binomial (ZINB) models the most appropriate to fit this kind of data. To Incorporate the spatial dimension into the count data models, Geographically Weighted Poisson Regression (GWPR), Geographically Weighted Negative Binomial Regression (GWNBR) and Geographically Weighted Zero-Inflated Poisson Regression (GWZIPR) have been developed, but the zero-inflation part of the negative binomial distribution is undeveloped in order to incorporate the overdispersion and the excess of zeros, as was at the beginning of the COVID-19 pandemic, whereas some places were having an outbreak of cases and in others places, there were no cases yet. Therefore, we propose a Geographically Weighted Zero-Inflated Negative Binomial Regression (GWZINBR) model which can be considered a general case for count data, since locally it can become a GWZIPR, GWNBR or a GWPR model. We applied this model to simulated data and to the cases of COVID-19 in South Korea at the beginning of the pandemic in 2020 and the results showed a better understanding of the phenomenon compared to the GWNBR model.