Comparing Spatial Scan Statistics for Zero-inflated Count Data

Abstract

In the analysis of count data such as crime and disease incidence, an excess of zero counts is commonly observed, limiting the applicability of the conventional Poisson model. To address this, we compare three approaches: the Scan-Poisson statistic, the Scan-ZIP (Zero-Inflated Poisson) statistic for zero-inflated data, and the Scan-ZINB (Zero-Inflated Negative Binomial) statistic, which additionally accounts for overdispersion. Simulation results revealed that the Scan-ZIP consistently outperformed the Scan-Poisson statistic in identifying zero-inflated data, with robust performance across different scenarios. The Scan-ZINB showed comparable or slightly inferior performance to Scan-ZIP in most simulations. To illustrate the real-world applicability of these methods, we applied them to arson incident data from 426 administrative districts in Seoul, spanning the years 2012 to 2021. The results indicated that both Scan-ZIP and Scan-ZINB outperformed Scan-Poisson in identifying significant clusters. The Scan-ZIP detected larger, high-risk clusters, particularly in regions with zero cases, due to its robust handling of zero-inflation. The Scan-ZINB, with the lowest AIC value, achieved an optimal balance between model fit and complexity, effectively capturing underlying data patterns while avoiding overfitting. In conclusion, although the Scan-Poisson method exhibits limitations in detecting clusters within datasets characterized by excess zeros and high variability, both Scan-ZIP and Scan-ZINB demonstrated their utility as more effective and robust tools for spatial cluster detection. These findings provide a foundation for further applications of zero-inflated models in areas such as public health, crime prevention, and environmental studies, where understanding spatial risk patterns is crucial.;본 연구는 영과잉 데이터를 다룰 수 있는 세 가지 공간 스캔 통계량(Scan-Poisson, Scan-ZIP, Scan-ZINB)의 성능을 비교 분석하였다. 영과잉 데이터는 0 값이 과도하게 나타나는 특성으로 인해 기존 포아송 기반 통계량의 적용에 한계가 있으며, 이를 해결하기 위해 영과잉 데이터를 처리하는 Scan-ZIP과 과산포를 추가적으로 고려하는 Scan-ZINB를 평가하였다. 시뮬레이션 결과, Scan-ZIP은 Scan-Poisson보다 일관되게 우수한 성능을 보였으며, Scan-ZINB는 과산포가 존재하는 데이터에서 더 우수한 결과를 나타냈다. 실제로 서울시 방화 사건 데이터를 활용한 분석에서도 Scan-ZIP과 Scan-ZINB가 Scan-Poisson보다 유의미한 클러스터를 효과적으로 탐지하였으며, 특히 Scan-ZINB는 가장 낮은 AIC 값을 기록하며 모델 적합성과 복잡성 간의 최적의 균형을 보였다. 본 연구는 영과잉 및 과산포 데이터 분석에서 Scan-ZIP과 Scan-ZINB의 강점과 유용성을 입증하였으며, 이는 공중보건, 범죄 예방, 환경 분석 등 다양한 분야에서 활용 가능성을 제시한다.