Integrative Analysis of Spatial Heterogeneity and Overdispersion of Crime with a Geographically Weighted Negative Binomial Model

Jianguo Chen,Lin Liu,Dongping Long,Chong Xu,Luzi Xiao

doi:10.3390/ijgi9010060

Abstract

Negative binomial (NB) regression model has been used to analyze crime in previous studies. The disadvantage of the NB model is that it cannot deal with spatial effects. Therefore, spatial regression models, such as the geographically weighted Poisson regression (GWPR) model, were introduced to address spatial heterogeneity in crime analysis. However, GWPR could not account for overdispersion, which is commonly observed in crime data. The geographically weighted negative binomial model (GWNBR) was adopted to address spatial heterogeneity and overdispersion simultaneously in crime analysis, based on a 3-year data set collected from ZG city, China, in this study. The count of residential burglaries was used as the dependent variable to calibrate the above models, and the results revealed that the GWPR and GWNBR models performed better than NB for reducing spatial dependency in the model residuals. GWNBR outperformed GWPR for incorporating overdispersion. Therefore, GWNBR was proven to be a promising tool for crime modeling.

Highlights

Due to the disparities of built environments and socio-demographic factors, the uneven distribution of crime across different neighborhoods has long been confirmed by many studies [1,2,3,4]
Routine activity theory proposed by Cohen and Felson is a theoretical framework commonly used in crime analysis [6], which states that the convergence of a motivated offender, a vulnerable victim, and a crime-prone place will lead to criminal offenses
Four models were developed to investigate the effect of overdispersion on crime analyses based on the above-mentioned methodology, including the negative binomial model (NB), geographically weighted Poisson regression model (GWPR), geographically weighted negative binomial regression model with local alpha, and geographically weighted negative binomial regression model with global alpha

Summary

Introduction

Due to the disparities of built environments and socio-demographic factors, the uneven distribution of crime across different neighborhoods has long been confirmed by many studies [1,2,3,4]. Among the many theories of crime geography, routine activity theory, and crime pattern theory are usually employed to explain the spatial agglomeration of criminal activity. Routine activity theory proposed by Cohen and Felson is a theoretical framework commonly used in crime analysis [6], which states that the convergence of a motivated offender, a vulnerable victim, and a crime-prone place will lead to criminal offenses. Proposed by Brantingham and Brantingham [7], crime pattern theory argues that crime is not randomly distributed over space and time, but presents a specific pattern of places where the intersection of offenders and victims are more vulnerable to crime. The above two theories effectively explain why crime is spatially concentrated and form ‘hot spots’ of criminal offenses

Methods

Results

Conclusion