Bayesian Spatio-Temporal Modeling for Analysing Lo

ORIGINALPAPERBayesianSpatio-TemporalModelingforAnalysingLocalPatternsofCrimeOverTimeattheSmall-AreaLevelJaneLaw•MatthewQuick•PingChanPublishedonline:25January2013SpringerScience+BusinessMediaNewYork2013AbstractObjectivesExploreBayesianspatio-temporalmethodstoanalyselocalpatternsofcrimechangeovertimeatthesmall-arealevelthroughanapplicationtopropertycrimedataintheRegionalMunicipalityofYork,Ontario,Canada.MethodsThisresearchrepresentsthefirstapplicationofBayesianspatio-temporalmodelingtocrimetrendanalysisatalargemapscale.TheBayesianmodel,fittedbyMarkovchainMonteCarlosimulationusingWinBUGS,stabilizedriskestimatesinsmall(censusdissemination)areasandcontrolledforspatialautocorrelation(throughspatialrandomeffectsmodeling),deprivation,andscarcedata.Itestimated(1)(linear)meantrend;(2)area-specificdifferentialtrends;and(3)(posterior)probabilitiesofarea-specificdifferentialtrendsdifferingfromzero(i.e.awayfromthemeantrend)forrevealinglocationsofhotandcoldspots.ResultsPropertycrimeexhibitedadecliningmeantrendacrossthestudyregionfrom2006to2007.Variationofarea-specifictrendswasstatisticallysignificant,whichwasapparentfromthemapof(95%credibleinterval)differentialtrends.Hotspotsinthenorthandsouthwest,andcoldspotsinthemiddleandeastoftheregionwereidentified.ConclusionsBayesianspatio-temporalanalysiscontributestoadetailedunderstandingofsmall-areacrimetrendsandrisks.Itestimatescrimetrendforeachareaaswellasanoverallmeantrend.Thenewapproachofidentifyinghot/coldspotsthroughanalysingandmappingprobabilitiesofarea-specificcrimetrendsdifferingfromthemeantrendhigh-lightsspecificlocationswherecrimesituationisdeterioratingorimprovingovertime.Futureresearchshouldanalysetrendsoverthreeormoreperiods(allowingfornon-lineartimetrends)andassociated(changing)localriskfactors.J.Law(&)M.QuickSchoolofPlanning,UniversityofWaterloo,200UniversityAvenueWest,Waterloo,ON,Canadae-mail:[e-mail]ndHealthSystems,UniversityofWaterloo,Waterloo,ON,CanadaP.ChanTrinityHallCollege,UniversityofCambridge,Cambridge,UK123JQuantCriminol(2014)30:57–78DOI10.1007/s10940-013-9194-1KeywordsProbabilitymappingCrimetrendsHotspotsBayesianhierarchicalmodelsSpatio-temporalSpatialIntroductionCrimetrendstatisticsreportwhethercrimehasincreased,decreased,orremainedconstantovertime(Willbach1938).Annualcrimereportsoftenusetables,graphs,and/ormapstoindicatepercentorratechangefrompreviousyears,butseldomusespatialstatisticalmethodstoanalysecrimetrends.Thisstyleofcrimetrendanalysisandreportingislimitedinconveyingacomprehensiveunderstandingofsmall-areachangesincrimeandisinef-fectivewhenusedtoinformlocalpoliceandcrimepreventioninitiatives.ThroughtheapplicationofBayesianspatio-temporalmethodstopropertycrimedataintheRegionalMunicipalityofYork,Ontario,thisresearchdemonstratesanovelmethodofanalysingsmall-areacrimetrendsthatenhancesunderstandingofcrimechangeovergeographicspaceandtime,andimprovestheapplicationofanalyticalresultstopoliceandcrimeprevention.Bothspatialandtemporallensesareusefulforstudyingcrimetrends.Broadly,researchintothespatialdimensionofcrimerecognizesthatcrimeratesshowsubstantialgeographicvariation(oftenreferredtoasspatialstructure,spatialdependence,orspatialautocorre-lation)becausetheyareaproductoflocalphysicalandsocialenvironments(Winsberg1993;GriffithsandChavez2004;Jenningsetal.2011).Studiesaddressingtemporalaspectsofcrimeinvestigatetime-basedcharacteristicssuchaschangestoagestructure(Levitt1999),unemploymentrates(Levitt2001),agingcriminalparticipants(OuseyandLee2007),orcriminalopportunity(Leitneretal.2011).Spatio-temporalanalysiscombinesspatialandtemporallensestoexaminevariationofriskoverspaceandtime,wherespatialunits(e.g.censusareas,neighborhoods)exhibitdistincttrendsovertime(GriffithsandChavez2004).Fewspatio-temporalstudieshaveanalysedspace–timeinteractionorspatio-temporalinteractioneffect.GrubesicandMack(2008)describedspatio-temporalapproachesincrimestudiesforidentifyinghotspotsastestsofspace–timeinteraction.Bernardinellietal.(1995)describedspatio-temporalinteractioneffectinhealthstudiesasvariationoftime-trendofhealthrisksacrossareas.Ingeneral,therehasbeenalackofspatio-temporalresearchinthecrimecontext,particularlyusingstatisticalmethodsthataddressbothspaceandtimeinthesameanalyticalmodelatalargemapscale.Instead,crimeanalysesareoftenexclusivelyspatialortemporal,ortreatspatialandtemporalaspectsasdistinctentitieswithoutstudyingspatio-temporalinterac-tion,forgoingtheabilitytounderstandifgeographicallyclosecrimetrendsaresimilarorwhetherthereisspace–timeclusteringafteradjustingforpurelyspatialandpurelytem-poraleffects(GrubesicandMack2008).Further,previousspatio-temporalstudiesincrimehaveoftenbeenconductedatasmallmapscale,likelybecausedatathatcontaininfor-mationaboutspecificcrimelocation,suchasstreetaddressesorpostalcodes,areinac-cessibletoresearchersduetoprivacyissues.Spatio-temporalanalysesatalargemapscalepresenttheopportunitytoaddresstheseshortcomings,uncoveringaccuratetrendsforpreciseareasandprovidingnovelinsightintotheaetiologyofcrime.Thisres