An empirical likelihood approach for detecting spatial clusters of continuous data

Abstract

AbstractSpatial scan statistics are an important tool for detecting and evaluating the statistical significance of spatial clusters and have widespread applications in various fields. The study proposes a new nonparametric spatial scan statistic based on the empirical likelihood method as an alternative to existing methods, for detecting clusters for continuous outcomes from unknown or skewed probability distributions. The existing methods are either based on distribution-free methods or likelihood ratio tests assuming a probability distribution. The proposed spatial scan statistic is based on the empirical likelihood method which remains distribution-free while allowing the use of likelihood methods. The performance of the proposed method was compared to the Mann–Whitney-based nonparametric scan statistic and the normal model-based scan statistic through a simulation study under varied scenarios as well as application on a real data. The proposed method had better positive predictive value compared to the Mann–Whitney-based scan statistic, and better sensitivity than the normal-based scan statistic. The methods had little to no difference in terms of power, with the proposed method performing much better in most scenarios. The number, order, location, and extent of the potential clusters detected from the rape crime data from India for the year 2011 varied across methods with certain similarities and differences. The Mann–Whitney and normal scan statistics detected more clusters in common with the proposed method than with each other. The proposed method serves as a good alternative and/or complementary method to existing spatial scan statistics for continuous outcomes when the underlying distribution is unknown or asymmetric.