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PathDependenceandTheValidationofAgent-basedSpatialModelsofLandUseDANIELG.BROWN,SCOTTPAGE,RICKRIOLO,MOIRAZELLNERandWILLIAMRANDInthispaper,weidentifytwodistinctnotionsofaccuracyofland-usemodelsandhighlightatensionbetweenthem.Amodelcanhavepredictiveaccuracy:itspredictedland-usepatterncanbehighlycorrelatedwiththeactualland-usepattern.Amodelcanalsohaveprocessaccuracy:theprocessbywhichlocationsorland-usepatternsaredeterminedcanbeconsistentwithrealworldprocesses.Tobalancethesetwopotentiallyconflictingmotivations,weintroducetheconceptoftheinvariantregion,i.e.,theareawhereland-usetypeisalmostcertain,andthuspathindependent;andthevariantregion,i.e.,theareawherelandusedependsonaparticularseriesofevents,andisthuspathdependent.Wedemonstrateourmethodsusinganagent-basedland-usemodelandusingmulti-temporalland-usedatacollectedforWashtenawCounty,Michigan,USA.Theresultsindicatethat,usingthemethodswedescribe,researcherscanimprovetheirabilitytocommunicatehowwelltheirmodelperforms,thesituationsorinstancesinwhichitdoesnotperformwell,andthecasesinwhichitisrelativelyunlikelytopredictwellbecauseofeitherpathdependenceorstochasticuncertainty.Keywords:Agent-basedmodeling;Land-usechange;Urbansprawl;Modelvalidation;ComplexsystemsIntroductionTheriseofmodelsthatrepresentthefunctioningofcomplexadaptivesystemshasledtoanincreasedawarenessofthepossibilityforpathdependencyandmultipleequilibriaineconomicandecologicalsystemsingeneralandspatialland-usesystemsinparticular(AtkinsonandOelson1996,Wilson2000,Balmann2001).Pathdependencearisesfromnegativeandpositivefeedbacks.Negativefeedbacksintheformofspatialdis-amenitiesruleoutsomepatternsofdevelopmentandpositivefeedbacksfromroadsandotherinfrastructureandfromservicecentersreinforceexistingpaths(Arthur1988,Arthur1989).Thus,asmallrandomcomponentinlocationdecisionscanleadtolargedeviationsinsettlementpatternswhichcouldnotresultwerethosefeedbacksnotpresent(AtkinsonandOleson1996).Concurrentwiththisawarenessoftheunpredictabilityofsettlementpatternshasbeenanincr
