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It is well established that offenders' routine activity locations (nodes) shape their crime locations, but research examining the geography of offenders' routine activity spaces has to date largely been limited to a few core nodes such as homes and prior offense locations, and to small study areas. This paper explores the utility of police data to provide novel insights into the spatial extent of, and overlap between, individual offenders' activity spaces. It includes a wider set of activity nodes (including relatives' homes, schools, and non-crime incidents) and broadens the geographical scale to a national level, by comparison to previous studies. Using a police dataset including n=60,229 burglary, robbery, and extra-familial sex offenders in New Zealand, a wide range of activity nodes were present for most burglary and robbery offenders, but fewer for sex offenders, reflecting sparser histories of police contact. In a novel test of the criminal profiling assumptions of homology and differentiation in a spatial context, we find that those who offend in nearby locations tend to share more activity space than those who offend further apart. However, in finding many offenders' activity spaces span wide geographic distances, we highlight challenges for crime location choice research and geographic profiling practice.
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ISPRSInt.J.GeoInf.2021,10,47.https://doi.org/10.3390/ijgi10020047www.mdpi.com/journal/ijgi
Article
ANationalExaminationoftheSpatialExtentandSimilarityof
Offenders’ActivitySpacesUsingPoliceData
SophieCurtisHam
1,
*,WimBernasco
2,3
,OlegN.Medvedev
1
andDevonL.L.Polaschek
1
1
TePunaHaumaruNZInstituteofSecurityandCrimeScience,TeKuraWhatuOhoMauriSchoolofPsy
chology,TeWhareWānangaoWaikatoUniversityofWaikato,Hamilton3240,NewZealand;
oleg.medvedev@waikato.ac.nz(O.N.M.);polascde@waikato.ac.nz(D.L.L.P.)
2
NetherlandsInstitutefortheStudyofCrimeandLawEnforcement(NSCR),1081HVAmsterdam,The
Netherlands;WBernasco@nscr.nl
3
DepartmentofSpatialEconomics,SchoolofBusinessandEconomics,VrijeUniversiteitAmsterdam,1081
HVAmsterdam,TheNetherlands
*Correspondence:sc398@students.waikato.ac.nz
Abstract:Itiswellestablishedthatoffenders’routineactivitylocations(nodes)shapetheircrime
locations,butresearchexaminingthegeographyofoffenders’routineactivityspaceshastodate
largelybeenlimitedtoafewcorenodessuchashomesandprioroffenselocations,andtosmall
studyareas.Thispaperexplorestheutilityofpolicedatatoprovidenovelinsightsintothespatial
extentof,andoverlapbetween,individualoffenders’activityspaces.Itincludesawidersetofac
tivitynodes(includingrelatives’homes,schools,andnoncrimeincidents)andbroadensthegeo
graphicalscaletoanationallevel,bycomparisontopreviousstudies.Usingapolicedatasetinclud
ingn=60,229burglary,robbery,andextrafamilialsexoffendersinNewZealand,awiderangeof
activitynodeswerepresentformostburglaryandrobberyoffenders,butfewerforsexoffenders,
reflectingsparserhistoriesofpolicecontact.Inanoveltestofthecriminalprofilingassumptionsof
homologyanddifferentiationinaspatialcontext,wefindthatthosewhooffendinnearbylocations
tendtosharemoreactivityspacethanthosewhooffendfurtherapart.However,infindingmany
offenders’activityspacesspanwidegeographicdistances,wehighlightchallengesforcrimeloca
tionchoiceresearchandgeographicprofilingpractice.
Keywords:homologyassumption;geographicoffenderprofiling;offenderactivityspace;police
data;routineactivitynodes
1.Introduction
Offenders’routineactivitylocations—wheretheylive,work,andcarryoutother
noncriminalactivities—playasignificantroleinshapingtheircrimelocations[1–3].Un
derstandingthenatureandspatialdistributionofindividualoffenders’activitylocations
thushasimportantimplicationsforcrimeandpolicingpolicyandpractice:forexample,
identifyingplacesthatindividualsareathigherriskofoffending,oridentifying,inpolice
investigations,suspectswhowouldbemorelikelytohavecommittedagivencrimeina
givenlocation[4].Yetlittleresearchtodatehasstudiedthefullrangeofoffenders’routine
activitylocations,oraddressedpracticallyimportantquestionssuchastheextentto
whichoffenders’activitylocationsaresharedorcanbedifferentiated,asweelaborate
below.
Manypolicejurisdictionsmaintaindatabaseswhichstorethedetailsofcallsforser
vice,criminalinvestigations,intelligencereports,arrests,stops/searchesandotherroutine
policeactivitiesthatinvolveinteractingwithmembersofthepublic[5–8].Thedetailsof
suchrecordscanincludeinformationaboutthelocationsofoffenses,incidents,police
Citation:CurtisHam,S.;Bernasco,
W.;Medvedev,O.N.;Polaschek,
D.L.L.Anationalexaminationofthe
spatialextentandsimilarityofof
fenders’activityspacesusingpolice
data.ISPRSInt.J.GeoInf.2021,10,
47.https://doi.org/10.3390/
ijgi10020047
AcademicEditor:MarcoHelbich
andWolfgangKainz
Received:4December2020
Accepted:18January2021
Published:23January2021
Publisher’sNote:MDPIstaysneu
tralwithregardtojurisdictional
claimsinpublishedmapsandinsti
tutionalaffiliations.
Copyright:©2021bytheauthors.Li
censeeMDPI,Basel,Switzerland.
Thisarticleisanopenaccessarticle
distributedunderthetermsandcon
ditionsoftheCreativeCommonsAt
tribution(CCBY)license(http://crea
tivecommons.org/licenses/by/4.0/).
ISPRSInt.J.GeoInf.2021,10,472of21
interactions,thehomeaddressesofthepartiesinvolvedandevenwheretheyworkor
attendschool.Providedthedatacontainslocationandtiminginformationwithsufficient
specificity,andcanbecollatedifstoredacrossmultipledatabases,itcouldbearichsource
ofinformationaboutoffenders’activityspaces(Thispaperfocusesonlocationswhere
offendershavecarriedoutroutineactivities,ortravelledbetweenthem,collectivelymak
inguptheir‘activityspace’[1].Therelatedconceptof‘awarenessspace’additionallyin
cludesplacesknownthroughsourcesotherthandirectexperience[1],whicharenotiden
tifiablefromthepresentdata.),particularlyforthosewhohavefrequentlycomeintocon
tactwithpoliceasoffenders,orasvictims,witnesses,ormembersofthecommunity.
However,suchdatahavenotyetbeenusedtostudyoffenders’activitylocationsother
thantheirresidentialaddressesandpriorcrimelocations[3,9].
Theaimsofthispaperarethereforetwofold:first,fromamethodologicalperspec
tive,toconsidertherangeofroutineactivitylocationsthatcanbeidentifiedusingthekind
ofpolicedatadescribedabove;second,toanswerseveralexploratoryresearchquestions
relatingtothenatureanddistributionofoffenders’activitylocationsasrevealedbythese
data.Weexaminethedistributionsofactivitylocationsofoffendersidentifiedforabur
glary,robberyorsexualoffenseovertimeframesofvaryinglengthspriortothemostre
centoffenseandgeographicunitsofanalysisofvaryingsizes.Wefocusoncrimesthat
typicallyinvolvesomeformofsearchforasuitablevictimortarget(ratherthanthetar
getingofaspecificvictimalreadyknowntotheoffender)whichisinfluencedbytheof
fenders’prioractivitylocations.Thesubsetofcrimetypesincludedherereflectamixture
ofenvironmentsandlanduses(residential,business/retail),motivations(material/non
material)andplanning(stronglyversusweaklypremeditated)andthusarelikelytobe
representativeofawidersetofcrimetypes.Wealsoexploretheextenttowhichtheavail
ableactivitylocationsoftheseoffendersdifferentiatebetweenthem.Thequestionofdif
ferentiationisparticularlyimportantforgeographicprofilingmethodsthatseektopre
dict,giventhelocationsofunsolvedcrimes,whomayhavecommittedthemorwherethe
offendermightbefound[10,11].Ifactivityspacesweresharedbymanyoffenders,they
wouldbeoflittleuseforprioritizingamongsuspects.
Webeginwithareviewofthesmallextantliteraturethathasexaminedoffenders’
routineactivityspacesandexpandontheconceptofdifferentiation.Wethenprovidede
tailsofthedatausedinthisresearchandthemethodsusedintheanalysesbeforepresent
inganddiscussingtheresults.Weconcludebyhighlightingthebenefitsandlimitations
ofthedataforbothresearchandpractice.
1.1.Offenders’ActivitySpaces
Understandingthenatureofoffenders’activityspacesbeyondtheirhomesisanim
portantresearchendeavor,givenwellestablishedlinksbetweentheiractivityspacesand
offenselocations.AsRoutineActivitiesTheoryasserts,crimerequiresaconvergenceof
motivatedoffendersandpotentialtargetsintimeandspace[12].Furthermore,asCrime
PatternTheoryexplains,thisconvergencehappenswhenandwheretheroutineactivities
ofoffenders(formingtheiractivityspace)overlapwithcrimeopportunities[1,2].Offend
ers’noncriminalandcriminalactivitiesalikeequipthemwithknowledgeofpossible
crimelocationsthatisbroughttobearonfuturedecisionsaboutwheretocommitcrime
[1,2].Studiesofaggregatecrimepatternsconfirmthatcrimeconcentratesinornearrou
tineactivitylocationslikelytobecommontomanyoffenders,suchascentralbusiness
districts,shoppingprecinctsandtransithubs[13,14].Atanindividuallevel,manystudies
demonstratethatpeoplearemorelikelytocommitcrimeclosertotheirhomethanfurther
away[15].Furthermore,interviewstudiesofsmallsamplesofoffendershavehighlighted
thatoffenderstendtocommitcrimesatorneararangeofotherroutineactivitylocations
suchaswork,friendsandfamilymembers’homes,recreationsites,orpriorcrimes[16–
22].StudiesusingDiscreteSpatialChoiceModelling(DSCM)haveevenquantifiedthe
increaseinoddsofalocationbeingchosenbasedonitsproximitytooffenders’previous
addresses,theirfamilymembers’currentorpreviousaddresses,andthelocationsoftheir
ISPRSInt.J.GeoInf.2021,10,473of21
previouscrimes,whencontrollingforproximitytotheirhome[3,9,23–26].Twofurther
DSCMstudies,bothonyoungoffenders,incorporatedadditionaltypesofactivitynodes
toconfirmthattheoddsofcrimeincreasewithproximitytoanyactivitynode[27,28].
However,fewstudieshavedescribed,quantitatively,offenders’routineactivity
spacesintermsofthenumberoflocationstheyfrequent,orthegeographicextentofthese
locations,overagiventimeperiod.Thosethathavevaryinlocation,cohort,andmethod,
butprovidearoughbaselinewithwhichtocomparethepresentstudy.Forexample,lo
cationtrackingdatafromfourteen19‐to44yearoldparoleesonGPSmonitoringinFlor
idarevealedthatoffendersvisited4nonhomenodes(specificsites)onaverage(range2
to6)duringtheweekpriortoreoffending[29].Theiractivityspacescoveredanaverage
of27milessquared(median12,range0.2to70).
IntheNetherlands,78youngoffendersaged1826whoparticipatedinanonlinesur
veyreportedvisiting6nodes(neighborhoods)onaverage(range1to15)inthemonth
precedingtheiroffenses[28].Theseincludedhome,school/work,friend/familyresidences
andleisureactivitynodes,withmostoffendersreportingatleastoneofeach.Themaxi
mumdistancebetweenanyindividualoffender’snodeswas200km(ofapossiblemaxi
mumdistancebetweenanytwoneighborhoodsintheNetherlandsof300km).Inanother
Dutchinterviewbasedstudy[27],7013‐to16yearoldswhooffendedinthesubsequent
4yearsreportedanaverageof7activitynodes(200m×200mcellsinamapgridcovering
theHague)ina4dayperiodprecedingtheinterview(median5,range1to15).Almost
75%oftheirtimewasspentatjusttwonodes(homeandtypicallyschool),producinga
relativelyshort(average3km)“radiusofgyration”,ameasureofthesizeofanindivid
ual’sactivityspaceweightedbytimespentineachnode.
Consideringnotthenumberorgeographicrangeofnodesbuttheiroverlapbetween
individuals,aUKstudyfoundthattherewasahighcorrelationbetweentheaggregated
selfreportedawarenessspacesof17prolificpropertyoffendersand13nonoffenders
fromthesamecounty[20].Inotherwords,thenodescommontomanyoffenderswere
alsocommontothegeneralpopulationinthestudyarea.Weexpandontheissueofcom
monalityversusdifferentiationinactivityspaceinthenextsection.
1.2.HomologyandDifferentiationinActivitySpaces
Ingeographicprofilingforcriminalinvestigations,differentiationbetweensuspects’
activityspaceswouldenableprioritizationamongsuspectswhencomparingsuspects’
knownactivitylocationswiththepredictedbase(s)oftheoffender[11,30].Differentiation
wouldmeanthatsuspectsfitthe“geographicprofile”tovaryingdegrees.Conversely,if
offenders’activityspacesarerelativelyhomogenous,itwouldbedifficulttoprioritize
amongthemanypotentialsuspectswhoseactivityspacesareallequallyconsistentwith
themhavingcommittedanoffense(s)inagivenlocation.
Thisissuehasbeenraisedinthebehavioralprofilingliterature.Theabilitytoinferan
offender’scharacteristicsfromattributesofthecrimereliesoncoreassumptionsofho
mologyanddifferentiation[31–33].Homologymeansoffenderssharingcertaincrimeat
tributeswillalsosharecertainpersonalcharacteristics;differentiationmeansdifferences
incrimeattributesindicatedifferencesinoffenderattributes.Themoredistinctive(i.e.,
differentiating)theattribute(s)—ofcrimeandcriminal—themorereliablysuspectpools
canbenarrowed[31,33].
Withrespecttothespatialdimensionofoffending,homologymeansthatoffenders
sharingthelocationsoftheircrimeswillalsoshareotherpartsoftheiractivityspaces.For
example,iftwoburglarscommitanoffenseinthesamestreet,homologymeanstheyare
morelikelytoliveinthesameneighborhood,attendthesameschool,orvisitthesame
shoppingcenter,ascomparedtotwoburglarsoffendingindifferentstreets.TheDSCM
studiesdiscussedabovearesuggestiveofhomologybetweenoffenders’crimelocations
andactivityspaces.Sinceactivitynodelocationspredictcrimelocations[27],offenders
withsimilaractivitynodelocationswould,logically,offendinsimilarlocations,having
gainedawarenessofthesamecrimeopportunities.However,thereversedoesnot
ISPRSInt.J.GeoInf.2021,10,474of21
logicallyfollow,thoughgeographicprofilingreliesoninferringpotentialactivitynode
locationsfromoffenselocations.Illustrativeofthispoint,Costanzoetal.[34]foundthat
offenderswithnearbyhomeaddressestendedtotravelinasimilardirectiontooffend,
butthatoffenderswithnearbyoffenseshadnotnecessarilycomefromsimilardirections
tooffend.
Exploringthelinkbetweencooffenders’activityspacesandcrimelocations,Lam
mers[35]foundthatoffensescommittedatthesameplaceandtime(i.e.,bycooffenders)
weremorelikelytobecommittedinaneighborhoodwhereatleasttwoofthecooffenders
hadlivedorcommittedapreviouscrime,thanelsewhere.However,thecooffending
pairssharedlessthan50%oftheirresidentialorprioroffenseneighborhoods.Tayebiet
al.[36]foundthatoffenderswhoweremorecloselyconnectedinacooffendingnetwork
livedclosertogetherandsharedmorehomeandpastoffenseneighborhoods(however,
Malmetal.[37]foundnocorrelationbetweennetworkproximityandhomeproximityin
acannabisproductionnetwork).Thus,pastorpresentcooffendingmayentailsimilarity
ofsome,butnotall,elementsofcooffenders’activityspaces.
Thereisalsoevidencethatoffendersmightbedifferentiatedbytheircrimeandrou
tineactivitylocations.Nearbycrimesaremorelikelytohavebeencommittedbythesame
offenderthandifferentoffenders[38–42].Thatallpeopleexhibithighlydistinctivespatio
temporalroutineactivitypatterns[43],suggeststhatamongoffenders,activityspacesmay
alsobedistinctive.
However,neithertheextenttowhichindividualoffenders’activityspacesareshared
(otherthanwithcooffenders),northeextenttowhichhomologyanddifferentiationare
presentintherelationshipbetweenoffenders’activityspacesandtheircrimelocations,
hasbeendirectlyexaminedbyanystudiestodate.
1.3.PresentStudy
Wethereforeaimedtoexploretherangeofroutineactivitylocationsthatcanbeiden
tifiedinpolicedataandtoanswerthefollowingresearchquestionsrelatingtothenature,
distributionandspatialsimilarity(ordifferentiation)betweenoffenders’activityspaces
asrevealedbythesedata.(1)Whatisthedistributionofthenumberactivitynodesper
offender?(2)Whatisthedistributionofactivityspacesizeperoffender?(3)Whatpropor
tionofoffenders’activitynodesaresharedwithotheroffenders?(4)Dooffenderswho
offendedincloserproximitytoeachotherhavesimilaractivityspacesprecedingtheof
fense,relativetooffenderswhooffendedindifferentlocations?(Thepresentresearchcon
siderspurelyspatialsimilarity,ratherthantheoverlapofoffenders’activityspaceinboth
timeandspace.Offenderswhohavefrequentedthesamelocationyearsapartcouldiden
tifythesamecriminalopportunitiestotheextentthatthoseopportunitiesreflectstable
featuresoftheenvironment.Futureresearchmightconsiderwhetheroffensescloseto
getherinbothtimeandspaceareassociatedwithactivityspaceoverlappinginbothtime
andspace,whichwasnotpossiblewiththepresentdata.)
2.MaterialsandMethods
2.1.Data
AlldatausedinthisstudywereextractedfromtheNewZealandPolicenational
crimedatabase(NIA;NationalIntelligenceApplication).First,acohortofoffenderswas
identified:asthosewhohadcommittedaresidentialornonresidentialburglary,commercial
orpersonalrobbery,orextrafamilialsexualoffensebetween2009and2018(detaileddefini
tionsoftheseandallotheritalicizedparametersareprovidedinSupplementaryMaterial
S1).Fromtheseoffenses,themostrecent(“reference”)offensewasidentifiedforeachof
fenderandeachoffensetype.Second,arangeofactivitylocationsassociatedwiththe
offenders,recordedbypolicewhererequiredforoperationalpurposes,wereextractedas
follows.(Herein‘offender’meansthepersonwhocommittedthereferenceoffense.This
isnotmeanttoimplythattheyweretheoffenderinreferencetoprioroffenseswherethey
ISPRSInt.J.GeoInf.2021,10,475of21
wereavictimorwitness,orpriornoncrimeincidents.Further,thelabels‘burglar’,‘rob
ber’and‘sexoffender’inthispaperareusedforexpediencyandrefersolelytothenature
ofthereferenceoffense,nottoprioroffensehistories.)
Offensedataincludednontrafficoffensescommittedbytheoffender.Incidentdata
includednontrafficoffensesinvolvingtheoffenderinanonoffendingrole(e.g.,witnessor
victim)andnontrafficnoncrimeincidentsinvolvingtheoffender(e.g.,domesticdisputes,
suspiciousbehavior,drunkanddisorderly).Offensesandincidentsdatedbackto2004
(olderrecordsarepatchyasnotallweretransferredduringachangeindatabases).
Addressdataincludedpastandpresentaddressesofvarioustypessuchashome,
work,“spokentoat”,“seenat”,and“arrestedat”.ManualinspectionofNIArecordscon
firmedthelattercategoriesincludedarangeofnodessuchasacquaintances’homes,com
mercialorpublicfacilities,andonstreetencounterswithpolice.
Familyhomeaddressdataincludedpast(duringtheoffender’slifetime)andpresent
homeaddressesoffamilymembers,includingintimatepartnerrelationshipsandfamily
relationships.Abroaderdefinitionoffamilywasincludedthanusedinpreviousstudies
[24,25],whichwererestrictedtoparents,childrenandsiblings.Theinclusionofextended
familyreflectstheimportantroleofwiderfamilyinmanyNewZealand(NZ)communi
ties(e.g.,Māori,PacificandAsiancultures[44]).Althoughmaximizingtherangeofactiv
itynodesextractedwasdesirable,theinclusionofintimatepartnerrelationships,which
canbetemporary,willalsohaveintroducedsomeerror:homelocationsofpartnersmay
pre‐orpostdatetherelationshipandthereforemaynothavebeenvisitedbytheoffender.
Lastly,dataontheschoolandothereducationalinstitutionsattendedbytheoffenders
wasalsoextracted,whererecorded.EmploymentdetailsrecordedinNIAtypicallyonly
includedacompanynamewithnospecificdetailsoflocation,branchoranyotherad
dress,precludingsufficientlycompleteoraccurategeocodingtoenabletheirinclusion.
Referenceoffenseandallactivitylocationdataexceptschool/educationincludedthe
geographiccoordinatesofthelocations’addresses.Addressesareautomaticallygeocoded
(allocatedcoordinates)withintheNIAsystemwhenaddressesareentered.School/edu
cationrecordsincludedonlytheinstitutionname,notaddressdetails,requiringtheselo
cationstobegeocodedbytheresearchers.ThiswascompletedinR[45]usingaGoogle
MapsAPItosearchfortheinstitutionnameandreturnitsaddressandcoordinates(then
transformedinArcGIS),asdescribedinSupplementaryMaterialS3.Thedatawerethen
preprocessedinRtoexcluderecordsconsideredtooimprecisespatiallyortemporallyto
includeintheanalysis.
PreprocessingstepsandfiltersaredetailedinSupplementaryMaterialS2,which
alsoreportsthenumberandpercentofrecordsfromeachdatasetthatwereexcludedwith
eachfilter.Theexclusionofrecordswithmissingorimprecisespatialortemporaldata
resultedintheretentionofbetween86.2%and97.0%oftheactivitylocationsineachda
taset.Theseproportionsexceedtheminimumgeocodinghitrates(completeness)sug
gestedbyrecentstudiestomaintainthespatialdistributionofthedata,consideringthe
typesofoffensesandsizeofthedataset[46,47].Theresultsofchecksongeocodingaccu
racyandprecisioninthedatafollowingtheexclusionsaredetailedinSupplementaryMa
terialS3.Over95%ofrecordsfromeachdatasetweregeocodedtothecorrectlocation.
Theactivitylocationswerethenfilteredtothosewhichpredatedthereferenceof
fense.SupplementaryMaterialS4providesdetailsastohowthedatesofoffenses,inci
dents,(family)addressandeducationrecordsweretreatedinidentifyingwhetherthey
were“prior”tothereferenceoffense.Thisfilterreflectsouraimofexploringthedata’s
potentialforcrimelocationchoiceresearchandinvestigativeuse.Crimelocationchoice
researchwouldlimitoffenders’activityspacetotheperiodbeforetheycommittherefer
enceoffensetostrengthencausalinterpretations(e.g.,excludereversecausation).Inpolice
investigations,onlyactivitylocationsknowntopolicepriortothereferenceoffensewould
beavailabletoinforminvestigativedecisions.Table1showsthesizeofeachdatasetrela
tivetoeachreferenceoffensecategoryfollowingtheabovefilters,expressedasthenum
berofuniquepersonlocations,wherealocationiseitheradiscreteeventinspaceand
ISPRSInt.J.GeoInf.2021,10,476of21
time(offenses/incidents)oranaddresswithoutaspecificrelatedeventrecord(offender
andfamilyaddresses,educationaddresses).Italsoshowstheproportionofoffendersfor
whomtherewerenoprioractivitynodesinthedata,andwhowerethereforeexcluded
fromtheanalysis.Table2providesbasicdemographicstatisticsfortheoffenderswith
activitynodesincludedintheanalysis,foreachoffensetype.
Table1.Samplesizeineachdatasetrelativetoeachreferenceoffensecategory.
ReferenceOffenseOffenders1PriorOffensesPriorIncidentsAddressesFamilyAddressesEducation%withnoNodes
Res.Burg.34,532171,97376,257516,506899,14716,0321.15
Nonres.Burg.21,155106,26540,314295,262493,83410,8971.60
Com.Rob.397522,450844661,023106,88027610.49
Pers.Rob.873743,39318,809144,423285,51052740.92
SexOffenses974917,54614,19485,413114,67719718.94
1Therewere60,229offenders,ofwhom11,459appearedintwooffensecategories,2540appearedinthree,424appeared
infour,and27appearedinallfiveoffensecategories.
Table2.Offenderdemographicstatistics
ReferenceoffenseMedianAge(IQR)%Male%Female
Res.Burg.21(13)83.3%16.6%
Nonres.Burg.18(12)88.0%12.0%
Com.Rob.19(8)87.7%12.3%
Pers.Rob.19(10)80.7%19.3%
SexOffenses27(24)96.8%3.2%
Forthepurposesofthepresentanalyses,allprioractivitynodeswerethencompiled
foreachoffenderandanylocations(i.e.,specificcoordinates)thatwereduplicated(e.g.,
bothahomeaddressandprioroffenselocation)wereremovedsuchthateachlocation
wasonlycountedonceperoffender.
2.2.AnalyticApproach
Theresearchquestionswereaddressedviaarangeofdescriptiveandinferentialsta
tisticalanalyses,usingthesoftwareR,asdescribedinturnbelow.
2.2.1.NumberofActivityNodes
Wemeasuredthenumberofactivitynodesperoffenderattwospatialresolutions:
distinctaddresscoordinatesanddistinctsmallcensusunits.Theformerenabledidentifi
cationofhowmanyexactlocationsaretypicallyrecordedforoffenders,whichwouldal
lowforfinergrainedanalysisandmappingofsuspects’activitylocationsduringinvesti
gations,wheretheaimistoidentifyandlocateoffenders.Censusorotheradministrative
unitsare,however,amoreusefulunitofactivityspacewhenassessingvariabilityinthe
activityspacesofanoffenderpopulation[48].Theycanalsobeconsideredaproxyfor
unmeasuredactivityspace:wedonotvisitplacesinisolationbuttendtoclusterourac
tivitiestogether;placesimmediatelyaroundorinbetweenactivitynodesaremorelikely
tobeinouractivityspacethanplacesfurtheraway[49–52].
Tomeasureactivitynodesdefinedassmallcensusunits,forcomparabilitywithother
studiesofoffenderactivityspaceweusedtheNZStatisticalArea1(SA1).SA1stypically
contain100–200residents.Outliersincluderemoteregionsandbodiesofwaterwithno
residentialpopulation;industrial,commercialorruralareaswithresidentialpopulations
under100;anddenselypopulatedareascontainingapartmentblocks,retirementvillages
andresidentialfacilitieswithpopulationsabove500.TheSA1shapefileandmetadata
weredownloadedfromhttps://datafinder.stats.govt.nz/layer/98761statisticalarea1
2019generalised/.Therewere29,879SA1s,withamedianareaof0.067km2(mean8.941
km2,range0.001km2–5758.384km2).(251SA1srepresentingbodiesofwater(inlets,
ISPRSInt.J.GeoInf.2021,10,477of21
coastlinesandlakes)wereexcludedfromtheareastatisticsasoutlierswithnolandarea.
AsasmallnumberofoffendernodepointsfellwithinsomeoftheseSA1stheywerere
tainedintheanalysis.)ThemediandistancebetweenthecenterofanSA1andthecenter
ofitsnearestneighborSA1was199m(mean760m,range11m–53.106km).SA1sthuslie
betweenthespatialunitsusedbyMentingetal.[28]—censusunitsaveraging0.68km2
and675residents—andBernasco’s[27]200m×200mgridcells.TheSA1sofreference
offenseandactivitylocations’coordinateswereidentifiedusingthesfpackageinR[53].
2.2.2.ActivitySpaceSize
ThenumberofSA1sinanoffender’sactivityspaceisanindicatorofrelativeactivity
spacesize,butitdoesnotcaptureitsgeographicalextent.Forexample,wereoffenders’
nodesconfinedtoasmalltown,orpartofacity,oranentiremetropolitanarea?Didthey
spanmultipletown/citiesnearbyoratoppositeendsofthecountry?Togaugethegeo
graphicrangeofoffenders’activityspaces,weusedasimpleindicatorofthedistanceover
whichtheiractivitynodesextended:thelengthofthediagonalofarectangle(bounding
box)encompassingallanoffender’sactivitynodes(specificcoordinates).Thisdistance
measureenabledfasterprocessing(ascalculablefromEastingandNorthingcoordinates
inmeters,withouttheneedtousespatialobjects,inR)andsimplerinterpretationinrela
tiontotheabovequestionsthanareameasuresofactivityspacesuchasminimumbound
ingpolygonsandstandarddeviationalellipses[54]ortheradiusofgyration[27].
2.2.3.SharedActivitySpace
Toidentifythedistributionofsharedactivityspace,weidentifiedwhichSA1swere
sharedbymultipleoffenders,andthencalculatedtheproportionofeachoffender’sSA1
nodesthatwereshared.Wetestedtwodefinitionsof“shared”:twoormoreoffendersper
SA1,andthetop25%most“popular”SA1s.ChecksoftheSA1ssharedbythehighest
numbersofoffendersshowedthesewere,unsurprisingly,SA1scontainingprisons,
courts,policestationsandcitycenters.
2.2.4.HomologyandDifferentiation
Previousstudiesexamininghomologyanddifferentiationbetweenoffenseattributes
andoffendercharacteristicshaveframedthequestionasatestofassociation:whether
similarity/differenceinoffenseattributescorrespondstosimilarity/differenceinoffender
characteristics[32,33,55].Weappliedthesameapproach,testingwhetheroffenderswho
offendedinnearbylocationsweremoresimilarintheiractivityspacethanoffenders
whoseoffenseswerefurtherapart(i.e.,whetherreferenceoffenseproximitycorrelated
withactivityspacesimilarity).Wefirstidentifiedpairsofoffenderswhohadatleastone
activitynodeeachandwhosereferenceoffensesfellinthesameTerritorialAuthority(TA)
boundary(i.e.,thesamecityorregion).TAsareadministrativeunitsreflectingthejuris
dictionsofNewZealand’s67localauthorities.Wethentookrandomsamplesofpairs,
separatelyforurban,citybasedTAsandruralTAsthatcoverlargeareascontaining
smallersettlements.Stratifyingtheanalysisbyurbanandruralgroupsensuredthatthe
correlationresultswerenotanartefactofurbanoffenders’crimesandactivitylocations
beingincloserproximityandruraloffenders’crimesandactivitylocationsbeingfurther
apart,duetothedifferenceindensityofcrimeopportunitiesandroutineactivitylocations
inurbanandruralenvironments.(TheUrbangroupincludedallCityCouncilTAs.Wel
lingtonwastreatedasasingleTAmadeupofWellingtonCity,LowerHuttCity,Upper
HuttCity,PoriruaCityandKapitiCoastDistrict.Althoughadministeredbydifferent
Councils,theseareasmakeupasingleconurbationreflectedincommutingandroutine
activitypatterns.TheRuralgroupincludedallotherTAs(DistrictCouncils).)Foreach
analysiswesampled10,000pairsandcomputedcorrelationsbetweenthedistancebe
tweenthepairs’referenceoffensesandthreemeasuresofthesimilarityofthepairs’
ISPRSInt.J.GeoInf.2021,10,478of21
activityspaces.Kendall’staubwasusedforallcorrelationsbecauseexploratoryanalyses
showedtheassumptionoflinearitywasnotmet.
Thesimilaritymeasureswereasfollows.First,wecalculatedthepercentageofthe
firstoffender’snodes(SA1s)thatweresharedwiththesecondoffender.Thismeasured
thedegreeofdirectoverlapbetweentheoffenders’activityspaces,withpercentagescores
above0indicatingatleastoneSA1incommon.Second,wecalculatedtheminimumdis
tancebetweenanyofthepair’sactivitynodes,usingspecificcoordinates.Third,wetook
themedianofthedistancesbetweeneachofthefirstoffender’snodesandthenearestof
thesecondoffender’snodes.Thelattertwomeasurescapturehowcloseinspacetheof
fenders’activitynodeswere,withoutnecessarilyfallingintothesameSA1s.Themini
mumdistanceindicateswhetheranyofthepair’snodeswereclosetogether;themedian
nearestneighbordistanceprovidesanindicationofoverallspatialproximity,whilere
ducingtheinfluenceofoutlierswhichcouldbeatgreatdistancesapart.ThemapsinFig
ure1illustratethecomplementarityofthesemeasures.Usingthreeanonymizedexamples
fromthedata,theyshowforthreepairsofoffendersthedistributionofactivitynodesin
relationtotheircrimelocationsandthemeasuresofspatialsimilarityofactivityspace
betweeneachpair.PleasenotethatinExampleBthepair’sreferenceoffensesaresoclose
togetherthattheirsymbolsoverlap;likewise,inExampleC,offender2hasanactivity
node(apriorcrime)inthesamelocationastheirreferenceoffensethusthesymbolsover
lap.
Figure1.Illustrationofactivityspacesimilaritymeasuresforthreepairsofoffenders:(a)withclosereferenceoffenses
andhighactivityspacesimilarityonallthreemeasures,(b)withclosereferenceoffensesandsomeactivityspacesimi
larity,dependingonmeasure,and(c)withdistantreferenceoffensesandlessactivityspacesimilarity
Wealsoinvestigatedwhetherhomologywasrelatedtocooffending(i.e.,theof
fenderpaircommittedthereferenceoffensetogether).Sinceveryfewoftherandompairs
werecooffenders(seeSupplementaryMaterialS5forproportions),wetookadditional
samplesofoffenderpairswhohadoffendedinthesamelocation(within100m)asco
offenders,andasindependentoffenders(n=1000persample).(Samplesof8,000were
takenwithreplacementandreducedtouniquepairs.Foroffenseswithsmallnumbersof
cooffendingpairs(smallestN=221)thismeantallpairswereincludedinthesample.
Thisanalysiswasrepeatedwithpairsofoffenderswhooffendedattheexactsamecoor
dinatesbutwerenotcooffenders.Althoughthesamplesizesweremuchsmaller(smallest
N=156),theresults(notreported)werecomparabletothoseforoffenderswhooffended
within100mofeachother:alldifferencesremainedstatisticallysignificant;effectsizes
werewithin±0.16ofthe100mresults.)Wethentestedwhetherreferenceoffenseco
ISPRSInt.J.GeoInf.2021,10,479of21
offendersdisplayedgreateractivityspacesimilaritythanthosewhooffendedinthesame
locationindependently.MannWhitneyUtestswereusedastheassumptionofnormality
wasnotmetforanyofthemeasures.
2.2.5.AnalysisDimensions
Allanalyseswereconductedforeachoffensetypeseparately.Giventhatcrimeloca
tionsaretheproductoftheconvergenceofoffenders’activityspacewithcrimeopportu
nities,andopportunitystructuresdifferfordifferentoffenses(e.g.,residentialandnon
residentialburglary),therelationshipbetweencrimelocationsandactivityspacecanalso
differbetweenoffensetypes.
Wealsoconsidereddifferenttimeframesofvaryingdurationprecedingthereference
offense.Activityspaceisdynamic:peoples’activityspacechangesasplacesareaddedor
stopbeingvisited[56].Lessrecentlyvisitedplaceshaveloweroddsofcrimelocation
choice[3,9,25].However,thetemporallimitonnodeinfluenceisnotknown,andsome
historicalnodesmaystillhaveabearing:childhoodnodescouldfeatureprominentlyin
offenders’“mentalmaps”;offendersmighthavereturnedtoliveatornearapastfamily
homewithoutthisbeingknowntopolice[57,58].Wethereforecalculatedactivityspace
measuresusingactivitynodesthatwereactive(i.e.,occurredorwereenddated)within
theyear,threeyears,fiveyears,tenyears,andmorethantenyearsprecedingthereference
offense.Homologyanalyseswererepeatedacross1yearand“ever”timeframes.
3.Results
3.1.NumberofActivityNodes
Figure2presentsthedistributionsofthenumberofactivitynodesperoffender,by
offensetypeandpreoffensetimeframe,forspecificcoordinates(top)andSA1s(bottom).
Thenumberofspecificlocationsperoffenderrangedfrom1to581andthedistributions
arehighlyskewed:mostoffendershaveasmallnumberofnodes,andasmallnumberof
offendershavemanynodes.Thenumberofnodesincreaseswiththelengthofthepre
offenseperiod:asistobeexpectedsincethemeasureiscumulative.Themedianswere
comparableforburglary(from14foroneyearto36“ever”)androbbery(16to43)but
smallerforsexoffenses(6to13).
ThenumberofSA1speroffenderfollowedmuchthesamedistributions,exceptin
theupperextremes.ThemediannumberofSA1speroffenderrangedfrom13/12(0–1y)
to29/29(“ever”)forresidential/nonresidentialburglary,14/15to32/24forcommer
cial/personalrobberyand5to11forsexoffenses.ThemaximumnumberofSA1sperof
fenderwas481.AsshowninFigure1,distributionsareverysimilarwhencomparingthe
topandbottomgraphs,thoughthetailsattheupperendofthedistributionaretruncated
whenspecificlocationsareaggregatedtoSA1resolution.Thissuggestsa)thatformost
offenders,theirfewnodesaredistributedamongdifferentSA1sandb)forthefewoffend
erswithmanynodes,manyofthosenodesareclusteredwithinSA1s.
(a)
ISPRSInt.J.GeoInf.2021,10,4710of21
(b)
Figure2.Distributionofactivitynodesperoffenderbyreferenceoffensetypeandtimeframeprecedingthereference
offensebasedonspecificcoordinates(a)andSA1censusunits(b).
3.2.ActivitySpaceSize
ToputthenumberofSA1nodesintoageographiccontext,49.3%ofoffenderSA1
nodeswerelocatedinthemostpopulatedurbanTAsinNZ:Auckland,Wellington,
Christchurch,andHamilton.ThenumbersofSA1speroffenderrepresentverysmallpro
portionsoftheseurbanareas,whichcontainbetween1449(Hamilton)and13680(Auck
land)SA1s.Forexample,13SA1srepresents0.89%ofHamilton’sSA1sand0.09%ofAuck
land’s;29represents2.00%and0.12%respectively;andthemaximumof421(iftheywere
allinthesamecity)represents29.05%.and3.08%.Theactivityspacesofoffendersasrec
ordedinpolicedata,therefore,aretypicallyconstrainedtoasmallportionofanygiven
urbanareainwhichtheyconducttheirroutineactivities.
Thedistributionsofactivityspaceranges,however,revealthattheseactivitiesare
frequentlydistributedacrossmultipleurbanareas(whilelimitedtosmallareaswithin
each),asshowninFigure3.Themediandistancerangewas267km/256kmforresiden
tial/nonresidentialburglaryfor1year(420km/395kmever),268km/319kmforcommer
cial/personalrobberyfor1year(417/457ever)and78kmforsexoffensesfor1year(202
kmever).Themaximumdistancerangewasbetween1400and1600kmforalloffense
typesandactivitynodetimeframes,representingnodesatoppositeendsofthecountry
(lengthwise).Interestingly,thesemaximaemergedearly,appearingintheoneyearpre
offenseactivityspacetimeframe.However,withincreasingpreoffensetimespans,there
wereincreasingnumbersofoffenderswhoseactivityspacesspannedmultiplecitiesat
greaterdistancesapart.
Figure3.Distributionofactivityspacerangeperoffenderbyreferenceoffensetypeandtimeframeprecedingthereference
offense.
3.3.SharedActivitySpace
Mostoffenderssharedmostoralloftheiractivitynodeswithatleastoneotherof
fender(Figure4,top).Thisisperhapsunsurprisinggiventhevolumeandgeographic
spreadofactivitynodes,whichwouldincreasethelikelihoodofsharedSA1s.Corre
spondingly,residentialburglars,withthehighestvolumesofactivitynodes,hadlarger
proportionsofSA1ssharedwithotherresidentialburglars,whilecommercialrobbersand
sexoffenders,withthelowestvolumesofactivitynodes,hadsmallerproportionsof
sharedSA1s.Alsoasexpected,theproportionofsharedactivityspaceincreasedasmore
activitynodeswereincludedwithincreasingtimepriortothereferenceoffense
ISPRSInt.J.GeoInf.2021,10,4711of21
(illustratedinFigure4bythedarkerlinesextendinghigherontheYaxisthanthelighter
lines,atupperlimitof100%ontheXaxis).
(a)
(b)
Figure4.Distributionofproportionofactivityspacesharedwithanyotheroffenders(a)andinthetop25%mostcom
monlysharedSA1s(b),byreferenceoffensetypeandtimeframeprecedingthereferenceoffense.
Eventheproportionofactivityspacefallinginthe25%mostcommonSA1swas
greaterthan50%formostoffenders(Figure3,bottom).Themedianswere68%/67%for
oneyearto68%/68%forresidential/nonresidentialburglary,58%/67%to69%/70%for
commercial/personalrobberyand52%–56%forsexoffenses.Theupturnsofthedistribu
tionsat0%and100%sharedreflectcaseswhereoffendersonlyhaveoneactivitynode,
meaningeitherallornoactivityspaceisshared.Notealsothatthenumberofoffenders
sharingthe25%mostcommonSA1sisrelativetooffensetype.Forexample,thetop25%
ofSA1sforresidentialburglaryoffendernodes“ever”weresharedby55ormoreoffend
ers;thetop25%ofSA1sforsexoffendernodes“ever”weresharedby9ormoreoffenders.
Overall,theseresultspointtoalackofdistinctivenessinoffenderactivityspacesrec
ordedinpolicedata,inthatanygivennodeislikelytobeshared.Thefollowinganalyses
provideinsightintowhetherthesharedportionsofindividuals’activityspaceareshared
withthesameordifferentoffenders.
3.4.HomologyandDifferentiation
Therewerestatisticallysignificantbutsmallcorrelationsbetweentheproximityof
offenders’referenceoffensesandthespatialsimilarityoftheiractivityspaces.Asshown
bythefittedregressionlinesinredinFigure5,broadly,thecloserthereferenceoffenses,
themoresharedactivityspace;thefartherawaythereferenceoffenses,thelessshared
activityspace.Thecorrelationsrangedfrom−0.07forurbansexoffenders’1yearpreof
fenseactivityspaceto−0.24forruralburglars’“ever”(seeSupplementaryMaterialS5for
fullresults).Thehighercorrelationsforruraloffendersonthismeasurearelikelyaprod
uctofthelargerSA1sinruralareas,increasinglythelikelihoodofoffensesandactivity
nodesfallingintothesameSA1.
Notably,theproportionofactivityspacesharedbetweenspecificoffenderpairsis
muchsmallerthanthatsharedwithoffendersingeneral(seeprevioussection),suggesting
heterogeneityinoffenders’activityspaces.InFigure5abouthalfoftheoffenderpair
pointsappearat0%ontheYaxes.Themedianpercentagesharedactivityspacewas0%
forallgroupsexceptruralresidentialburglars(2.1%),ruralcommercialrobbers(3.0%)
ISPRSInt.J.GeoInf.2021,10,4712of21
andruralpersonalrobbers(4.5%).Almostnooffenderpairsshared100%oftheiractivity
space.
Figure5.Proportionofactivityspacesharedbetweenpairsofoffendersbydistancebetweentheirreferenceoffenses.
AsFigure6shows,tosomeextent,thecloseranytwooffenders’referenceoffenses,
theclosertogethertheirnearestactivitynodes;thefartherawaytheiroffenses,thefarther
aparttheirnearestnodes.Thecorrelationsrangedfrom0.14forurbancommercialrob
bers’preoffenseactivityspace“ever”,to0.29forruralburglars’1yearpreoffenseactiv
ityspace(seeSupplementaryMaterialS5forallresults).
Figure6.Minimumdistancebetweennearestactivitynodesbydistancebetweenreferenceoffenses.
AsshowninFigure7,therewasageneraltendencythatthecloseranytwooffenders’
referenceoffenses,theclosertheiractivitynodesonaverage;thefartherawaytheirof
fenses,thefartheraparttheirnodes.Thecorrelationsrangedfrom0.15forruralcommer
cialrobbers’preoffenseactivityspace“ever”,to0.28forurbanburglars’1yearpreof
fenseactivityspace(seeSupplementaryMaterialS5forallresults).
ISPRSInt.J.GeoInf.2021,10,4713of21
Figure7.Mediandistancebetweennearestactivitynodesbydistancebetweenreferenceoffenses.
Correlationswereslightlyweakerforthemediannearestnodedistancethanthemin
imumnodedistanceforruraloffenders.Incontrast,correlationswereslightlystronger
forthemediannearestnodedistanceforurbanburglaryandrobberyoffenders.These
smalldifferencesarepotentiallyexplainedbythelongerdistancesbetweennodesforrural
offenders;urbanoffenders’nodeswouldbeclosertogether.
Burglarsshowedthestrongesthomologybetweenoffenseproximityandactivity
spacesimilarity,withverysimilarresultsforresidentialandnonresidentialburglars.
Likewise,therewerenearidenticalresultsforcommercialandpersonalrobbers,bothdis
playinglesshomologythanburglars.Sexoffendersshowedtheleasthomologyasmeas
uredbypercentsharedactivityspacebutmorethanrobbersintermsofthedistancebe
tweenactivitynodes.
Ofpairsofoffenderswhooffendedinthesamelocation,cooffenderssharedmore
activityspace,andhadmoreproximalactivitynodesthanindependentoffenders.Alltests
ofdifferencebetweencooffendersandothersamelocationoffenderswerestatistically
significant,withsmalltomoderateeffectsizes(seeSupplementaryMaterialS6forfull
results).Onaverage,robberyandresidentialburglarycooffenderssharedatleastone
exactlocationnode(specificcoordinates)inthe“ever”timeframe,asindicatedbymedian
minimumnodedistancesof0.Theminimumdistancebetweennodeswasunder200m
onaverageforburglaryandrobberycooffenders,andunder500mforindependentbur
glarsandrobbers.Cooffendingandindependentsexoffenderswerelesslikelytoshare
anynodes(specificcoordinatesorSA1s);theirnearestnodeswerealsofurtheraparton
average(cooffenders:50–540m,independent:280m–1.86km).Notably,evenamongco
offenders,themediandistancefromeachofonecooffender’snodestothenearestofthe
othercooffender’snodeswasmuchlonger,onaverage,thantheminimumdistancebe
tweentheirnodes.
Collectivelytheseresultssuggestthatoffenderswhooffendinspatiallysimilarloca
tionstendtobespatiallysimilarinpartsoftheiractivityspace,thoughnotnecessarilyin
itsentirety.Furthermore,thesehomologyresultsarenotsolelyattributabletocooffend
ing.However,wealsoconfirmedthatcooffendersdisplayedgreateractivityspacesimi
laritythanoffenderswhooffendedinthesamelocationseparately.
4.Discussion
Weusedroutinelycollectedpolicedatatoprovideinsightintooffenders’activity
spacesintermsofthenumberofactivitynodes,theirgeographicrange,andtheextentto
whichtheyaresharedbetweenordifferentiateoffenders.Webelievethistobethelargest
andmostcomprehensivestudyofoffenderactivityspacetodate,consideringthefre
quencyandtypesofactivitynodesincluded.
ISPRSInt.J.GeoInf.2021,10,4714of21
Onthesurfacetheoneyearactivitynodedistributionsappearcomparabletothere
sultsofRossmoetal.’s[29]studyofUSparoleesandMenting[28]andBernasco’s[27]
studiesofyoungDutchoffenders,consideringthedifferenttimeframesinvolved.Ourme
dianswere13to15forburglary/robberyand5forsexoffenses,fornodesthatwerecurrent
duringtheyearpriortothereferenceoffense,comparedwith47nodesintheabovestud
iesovermuchshortertimeframes.However,ourdistributionswerewiderandappeared
moreskewed:aminorityofoffendershadnoprioractivitynodesonrecord;manyoffend
ershadfewnodes;afewhadverymany.Thisresultislikelyacombinationofbothmiss
ingnessandreality:wehavemorecompletedataforsomeindividualsthanforothers,
andsomeindividualsgenuinelyhavemoreactivitynodesthanothers,asfoundincrimi
nalcohortsinthe3studiesaboveandinthegeneralpopulation[51,56,59,60].Futurere
searchcouldhelpestablishtheextentof(in)completenessbycomparingpolicedataatan
individuallevelwithalternativedatasourcessuchassurveysorGPSdataasusedinthe
studiesabove.
Thattheactivityspacesfrequentlyspannedmultipleurbanareasisconsistentwith
thefewNZstudiesofthedistancesbetweenoffenders’homeaddressesandtheiroffenses,
andofthemobilityofNewZealandersingeneral.InNZ,thehomecrimedistancesofsex
offenderstendtobelongeronaveragethanoverseas,withhigherproportionsof“com
muter”offenderswhosehomesareoutsidetheradiusoftheiroffenses[61–64].Davidson’s
[65]studyofChristchurchburglars’homecrimedistancesfoundmoregeographically
constrainedpatternsbutmaynotrepresentcontemporarytrends,givenchangesinsocie
taltravelpatternsandmobility.In21stCenturyNewZealand,peoplemovefrequently
[66],familyandfriendscanbewidelydispersedacrossdifferenttownsandcities,and
domestictravelbycarorplaneiscommon,despitethelongdistancesinvolved[67–72].
Theinclusionofprisonsasactivitynodes,sometimesrecordedintheaddressdata,would
alsohavecontributedtothesedistancesbecauseoffendersmaybetransferredtoprisons
alongwayfromtheircommunity;theymayalsonotreturntothesamecommunityon
release[73](Prisonaddresseswerenotalwaysreadilyidentifiableinthedata,precluding
acomprehensiveinvestigationintotheextenttowhichtheyaccountedforwideactivity
spaceranges.).Itisnosurprise,therefore,thatNZoffenders’activityspacesspanned
muchlongerdistancesthanthoseoftheoffendersstudiedbyRossmoetal.[29],Menting
[28]andBernasco[27],giventhesestudiesweremoregeographicallyandtemporallycon
strained,andinvolvedcohortswithlikelymorelimitedmobility(offendersonGPSmon
itoringandyoungpeople).However,theextenttowhichourresultsareuniquetoNew
Zealandorindicatethatoffenderpopulationshavewideractivityrangesthancaptured
bystudieswithsmallerstudyareaswarrantsfurtherinvestigation.Weencouragefuture
studiesofoffenderactivityspaceinothercountriestowidentheirspatialscope.
Theanalysesofthenumberandgeographicrangeofactivitynodesrevealpotential
andproblemsfortheuseofthisdatainresearchandpractice.Intermsofvolume,thedata
arepromising:therewereavarietyofactivitynodesbeyondhomeaddressesavailablefor
theburglary,robberyand—toalesserextent—sexoffendersincludedinthisstudy.There
wasalsoconsiderableinformationgainwhenextendingthetimeframetolessrecentac
tivitynodes(burglarymedian29nodes,robbery34,sexoffenses11),thoughitremains
forfutureresearchtoexplorewhetherthisadditionalinformationyieldsanysignal:we
donotyetknowwhetherthese“older”activitynodesbearonthelocationsoffutureof
fenses.Incontrast,thedistributionswereverysimilarregardlessoftheunitofanalysis,
whichmaypartlyreflectthesmallsizeofSA1sintheurbanareasinwhichactivitynodes
wereconcentrated.Researchandanalysismaythereforebenefitfromtheuseofaggregate
spatialunitsofSA1sizewithoutmuchlossofinformation,atleastinurbanareas.
Thegeographicspanoftheoffenders’activityspacesindicatesapotentiallimitation
ofthisdata.Giventhatoffenders’activitynodeswereoftenwidelydispersed,ahighpro
portionofthesenodesarelikelytohavelittlebearingontheirchoiceofcrimelocationsat
amicrogeographicorneighborhoodlevel.Theremayevenbenoactivitynodesknown
topoliceinproximitytooffenders’latestoffenselocations.Incrimelocationchoice
ISPRSInt.J.GeoInf.2021,10,4715of21
research,ifthedatadonotinclude—withsufficientfrequency—themoreproximalactiv
itynodeslikelytohaveinfluencedagivencrimelocationchoice,modelsmayfailtoiden
tifyrelationshipsbetweenactivitynodesandcrimelocations.Incrimeinvestigations,
thereispotentialtomisspossiblesuspectsbynarrowlyfocusingonthosewithlocalnodes
inpolicedata,highlightingtheimportanceofsupplementingpoliceinformationwith
othersourcesofinformationonsuspects’activitynodes,beitthroughdatasharingagree
mentswithotheragenciesoronanindividualbasisfornamedsuspectsinagiveninves
tigation.
Anygivenactivitynode(SA1)waslikelytobesharedwithotheroffenderswhohad
committedthesamereferenceoffense,thoughthesenodeswerenotnecessarily“active”
atthesametime.ThisresultisconsistentwithHartandcolleagues’[60]findingthat80%
ofthepathsbetweenyoungAustralians’activitynodeswereshared.Themostfrequently
sharednodesreflectedplacesexpectedtohavehighnumbersofoffendersresidingorvis
iting(prisons,policestations,courthouses)orhighnumbersofpeopleingeneral(con
sistentwiththefindingsofMentingetal.[20]).Thelatterwouldgeneratemoreactivity
noderecordsinpolicedatathroughhigherlevelsofcrimeopportunityandhigherodds
ofencounteringpoliceduringproactivepatrols.
Comparinganytwooffenders,however,showedmuchlessoverlapbetweentheir
particularactivityspaces,signalingconsiderableindividualdifferencesinoffenders’rou
tineactivitypatternsascapturedinthisdata.Thehomologyanddifferentiationresults
suggestthatthoseroutineactivityspaceswere—marginally—morelikelytoconvergethe
closertogetheroffenders’latestoffenseswere.Ourresultsthusprovideevidenceofa
smalldegreeofspatialhomologyanddifferentiation,andsomeinsightsintoitscauses.
Forexample,referenceoffensecooffendershadgreateractivityspacesimilaritythan
offenderswhooffendedinthesamelocationbutindependently.Onepotentialexplana
tionforthisfindingisthatitreflectscooffenderswhohavealsocommittedothercrimes
togetherinthepast,andwhothussharepriorcrimenodes.Otherpotentialexplanations
reflectpossiblefamilialorsocialconnectionsbetweencooffenders.Onoccasion,coof
fendersmaybefamilymembers[74,75],whomaythereforesharehomeaddresses,family
homeaddress,orschoolnodes.However,morefrequently,cooffendersareconnected
socially[76,77].Humanmobilitystudieshaveshownthatpeoplemorecloselyconnected
inasocialnetworkhavemoresimilaractivityspacesthanthosewhoarenotsociallycon
nected[78–81].Cooffenders’socialtiescouldbeaproductoflivingincloseproximityor
attendingthesameschool,andbothacauseandeffectofsharing“hangout”nodes
[77,82,83].InNZ,aselsewhere,cooffendingcanoccurasapartofmembershipofgangs,
fromthefluid,looselyconnectedstructuresofyouthgangs,tomorehierarchicalorga
nizedcrimegroups[84–88].Manyyouthgangsalignthemselvestoparticularneighbor
hoodsreflectiveofthesharedactivityspaceoftheirmembers,andmoreformalizedgangs
arearrangedintolocal“chapters”[84–86].ConsistentwithLammers’study[35],however,
cooffendersdidnotsharemostoftheiractivitynodes.
However,sincecooffendersonlymadeupasmallproportionofoffenderpairsused
forthehomologycorrelations(andexcludingthemmadenodifferencetotheresults),
othermechanismsmustbeatplay.Forexample,thosewhoshareactivityspacearelikely
tobecomeawareofthesamecriminalopportunities;thosewithdifferentactivityspaces
areexposedtodifferentopportunities.Socialnetworksalsoplayarole:previouscooffend
ers(whosharepriorcrimenodes)shareinformationwitheachotheraboutcrimeoppor
tunitiesthatinfluenceswheretheyoffendinthefuturenotonlytogetherbutseparately
[89,90].
Robberyoffendersdisplayedlesshomologythanburglars.Thiscouldbeexpected
sincerobberytendstoconcentrateincommercialareaswithhighnumbersofpotential
targets[13,91,92],whichwouldattractpotentialoffenderswithdisparateresidential
nodes[2,34].Thathomologywasstillpresentmayreflecttherangeofnodesinthedata:
offenderscommittingrobberiesinthesamecommercialareamayalsohavecommitted
prioroffensesorhavehadpriorinteractionswithpoliceinthevicinity.
ISPRSInt.J.GeoInf.2021,10,4716of21
Thosecommittingsexoffensesappeartobeamorespatiallyheterogenousgroup,
alsodisplayinglessspatialoverlaporproximityintheiractivityspaces.Thismightbean
effectoftherebeingfewernodesinthedatasetfortheseoffenders,whichwouldmean
lesschanceoffindingoverlappingorproximalnodes.Itmightalsobeaneffectofthe
heterogenousnatureoftheseoffenses.Thesexoffensesincludedawiderangeofbehav
iors,fromindecentexposuretorape,andincludedoffensesagainstchildrenandadults.
Theycouldhaveoccurredattheoffender’shome,thevictim’shome,orelsewhere[93–
97].Sexoffenders’strategiesforidentifying,approaching,andattackingvictimsvary
widelyfromextendedgroomingtoopportunistic“blitz”attacks[98–102].Offenders
mightidentifytheirvictimsthroughsocialnetworks(onlineoroffline)orsearchforvic
timsintargetrichenvironmentssuchasnearschoolsornighttimeeconomydistricts
[94,96,97,102–104].Allthesefactorswouldleadtovariationintherelationshipbetween
offenders’activityspacesandtheircrimelocations.Furthermore,socialconnectionand
sharingofinformationbetweensexoffenders,suchasaboutthelocationsofcriminalop
portunities,appearstobelesscommonthanwithpropertycrime[97],whichwouldre
ducenetworkdrivenhomologyeffects.Futureresearchmightseektoisolatespatialho
mologyeffectsfordifferentsubtypesofsexoffenders.
Severallimitationsofthedataarealsoworthconsideringininterpretingourresults.
First,thedataonlyidentifiescooffenderswheretherewassufficientevidencetoproceed
againsteachoffender.Insomecases,multipleoffendersmayhavebeeninvolvedina
crimebutnotrecordedasoffendersduetoalackofevidence.Furthermore,offenderpairs
wereonlyidentifiableascooffendersiftheoffensewasbothoffenders’reference(i.e.,
latest)offense.Offenderpairswouldnotbeidentifiedascooffendersifonehadcommit
tedasubsequentoffense.Totheextentthatanycooffenderswerethustreatedashaving
offendedindependently,thedifferencesbetweencooffendersandindependentoffenders
willhavebeenunderestimated.
Second,thedatawerenotsystematicallyrecorded;theywereonlyonfilewherecol
lectedforoperationalpurposes.Asnoted,someoffendershadmorecompleterecords,
representingmoreoftheirroutineactivityspace.Ourconclusionsarethereforelimitedto
offenders’activityspacestotheextentidentifiablebyroutinelycollectedpolicedata.
Anadditionalcaveatisthatnotallactivityspaceisequalwithrespecttocrimeloca
tionchoice.Activitynodesthataremorerecent,morefrequentlyvisited,andhavebeen
inactivityspaceforalongertimehavestrongerassociationswithcrimelocations
[27,28,105],asdoactivitynodesthatprovidethemostrelevantknowledgeofcriminal
opportunity:priorcrimesofthesamenature[26,106].Wecouldthereforeexpectgreater
spatialsimilarityinthosepartsofoffenders’activityspacesthathavehadthegreatest
influenceinproducingsimilarityoftheircrimelocations.Indeed,ourresultssuggestthat
offenderswhooffendinspatiallysimilarlocationsarespatiallysimilarinpartsoftheir
activityspace.Furtherresearchwouldbeneededtodetermine,withthepresentdataset,
whichactivitynodesaremostpredictiveofcrimelocations,andwhetherhomologyeffects
arelargerwhenactivityspaceisisolatedto,orweightedby,thesemostinfluentialactivity
nodes.
5.Conclusions
Ourexplorationofpolicedataonawiderrangeofactivitynodesthanincludedin
previousstudiessuggeststhatgeographiccrimeanalysisandresearchcouldbenefitfrom
theuseofsuchdatasets,thoughwithsomecaution.Ourfindingsinrelationtothedis
tanceswithinandbetweenoffenders’activitynodes—andtheimplicationswehavehigh
lightedforresearchandpractice—arelikelytogeneralizetoothercountrieswithsimilar
levelsofinternalmobilityanddispersedpopulations(atbothmicroandmacrogeo
graphicscales).Inaddition,ourfindingsinrelationtothesparsity,andheterogeneity,of
sexoffenders’activitynodesinthisdataarealsolikelytoapplytoequivalentdatasetsin
otherjurisdictions.However,despitetheselimitations,thedataprovidednewdirectevi
denceoftheapplicabilityofthehomologyanddifferentiation“profilingassumptions”in
ISPRSInt.J.GeoInf.2021,10,4717of21
thegeographicprofilingcontextofoffenders’offenselocationsandactivityspaces.We
encouragefurtherresearch,withdatafrompoliceandalternativesources,intothespecific
elementsofactivityspacethatdisplaygreaterhomologyanddifferentiationwithrespect
tooffenders’crimelocations,andwhichcouldfurthersupportgeographicprofilingby
enablingspecificnodesofpotentialsuspectstoreceivemoreweightinprioritizationde
cisions.
SupplementaryMaterials:Thefollowingareavailableonlineatwww.mdpi.com/2220
9964/10/2/47/s1,DocumentS1:Dataparameterdefinitions;DocumentS2:Datafiltersandsample
attrition;DocumentS3:Geocodingprocess,accuracyandprecision;DocumentS4:Useofdatein
formationinidentifying‘prior’activitynodes;DocumentS5:Offensedistanceandactivityspace
similaritycorrelations;DocumentS6:Cooffenderandothersamelocationoffendercomparisons.
AuthorContributions:Forresearcharticleswithseveralauthors,ashortparagraphspecifyingtheir
individualcontributionsmustbeprovided.Thefollowingstatementsshouldbeused“Conceptual
ization,SophieCurtisHam;methodology,SophieCurtisHam,WimBernasco,OlegN.Medvedev,
DevonL.L.Polaschek;software,SophieCurtisHam;validation,SophieCurtisHam;