Analyzing car thefts and recoveries with connections to modeling origin–destination point patterns

Abstract

For a given region, we have a dataset composed of car theft loca-tionsalongwithalinkeddatasetofrecoverylocationswhich,dueto partial recovery, is a relatively small subset of the set of theftlocations. For an investigator seeking to understand the behaviorof car thefts and recoveries in the region, several questions areaddressed. Viewing the set of theft locations as a point pattern,can we propose useful models to explain the pattern? Whattypes of predictive models can be built to learn about recoverylocation given theft location? Can the dependence between thepoint pattern of theft locations and the point pattern of recoverylocations be formalized? Can theflowbetween theft sites andrecovery sites be captured?Origin–destination modeling offers a natural framework forsuch problems. However, here the data is not for areal unitsbut rather is a pair of dependent point patterns, with the re-covery point pattern only partially observed. We offer modelingapproaches for investigating the questions above and apply theapproaches to two datasets. One is small from the state of Nezain Mexico with areal covariate information regarding populationfeatures and crime type. The second, a much larger one, is fromBelo Horizonte in Brazil but lacks potential predictors.For a given region, we have a dataset composed of car theft loca-tionsalongwithalinkeddatasetofrecoverylocationswhich,dueto partial recovery, is a relatively small subset of the set of theftlocations. For an investigator seeking to understand the behaviorof car thefts and recoveries in the region, several questions areaddressed. Viewing the set of theft locations as a point pattern,can we propose useful models to explain the pattern? Whattypes of predictive models can be built to learn about recoverylocation given theft location? Can the dependence between thepoint pattern of theft locations and the point pattern of recoverylocations be formalized? Can theflowbetween theft sites andrecovery sites be captured?Origin–destination modeling offers a natural framework forsuch problems. However, here the data is not for areal unitsbut rather is a pair of dependent point patterns, with the re-covery point pattern only partially observed. We offer modelingapproaches for investigating the questions above and apply theapproaches to two datasets. One is small from the state of Nezain Mexico with areal covariate information regarding populationfeatures and crime type. The second, a much larger one, is fromBelo Horizonte in Brazil but lacks potential predictors.