倾向评分配对简介.ppt

IntroductiontoPropensityScoreMatching AReviewandIllustration ShenyangGuo Ph D SchoolofSocialWorkUniversityofNorthCarolinaatChapelHillJanuary28 2005ForWorkshopConductedattheSchoolofSocialWork UniversityofIllinois Urbana Champaign NSCAWdatausedtoillustratePSMwerecollectedunderfundingbytheAdministrationonChildren Youth andFamiliesoftheU S DepartmentofHealthandHumanServices FindingsdonotrepresenttheofficialpositionorpoliciesoftheU S DHHS PSManalyseswerefundedbytheRobertWoodJohnsonFoundationSubstanceAbusePolicyResearchProgram andbytheChildren sBureau sresearchgrant Resultsarepreliminaryandnotquotable Contactinformation sguo email unc edu Outline Day1Overview WhyPSM HistoryanddevelopmentofPSMCounterfactualframeworkThefundamentalassumptionGeneralprocedureSoftwarepackagesReview illustrationofthebasicmethodsdevelopedbyRosenbaumandRubin Outline continued ReviewandillustrationofHeckman sdifference in differencesmethodProblemswiththeRosenbaum Rubin smethodDifference in differencesmethodNonparametricregressionBootstrappingDay2Practicalissues concerns andstrategiesQuestionsanddiscussions PSMReferences Checkwebsite http sswnt5 sowo unc edu VRC Lectures index htm Linktofile Day1b doc WhyPSM 1 Need1 AnalyzecausaleffectsoftreatmentfromobservationaldataObservationaldata thosethatarenotgeneratedbymechanismsofrandomizedexperiments suchassurveys administrativerecords andcensusdata Toanalyzesuchdata anordinaryleastsquare OLS regressionmodelusingadichotomousindicatoroftreatmentdoesnotwork becauseinsuchmodeltheerrortermiscorrelatedwithexplanatoryvariable WhyPSM 2 Theindependentvariablewisusuallycorrelatedwiththeerrorterm Theconsequenceisinconsistentandbiasedestimateaboutthetreatmenteffect WhyPSM 3 Need2 RemovingSelectionBiasinProgramEvaluationFisher srandomizationidea Whethersocialbehavioralresearchcanreallyaccomplishrandomizedassignmentoftreatment ConsiderE Y1 W 1 E Y0 W 0 AddandsubtractE Y0 W 1 wehave E Y1 W 1 E Y0 W 1 E Y0 W 1 E Y0 W 0 Crucial E Y0 W 1 E Y0 W 0 Thedebateamongeducationresearchers theimpactofCatholicschoolsvis vispublicschoolsonlearning TheCatholicschooleffectisthestrongestamongthoseCatholicstudentswhoarelesslikelytoattendCatholicschools Morgan 2001 WhyPSM 4 Heckman Smith 1995 FourImportantQuestions Whataretheeffectsoffactorssuchassubsidies advertising locallabormarkets familyincome race andsexonprogramapplicationdecision Whataretheeffectsofbureaucraticperformancestandards locallabormarketsandindividualcharacteristicsonadministrativedecisionstoacceptapplicantsandplacetheminspecificprograms Whataretheeffectsoffamilybackground subsidiesandlocalmarketconditionsondecisionstodropoutfromaprogramandonthelengthoftimetakentocompleteaprogram Whatarethecostsofvariousalternativetreatments HistoryandDevelopmentofPSM Thelandmarkpaper Rosenbaum Rubin 1983 Heckman searlyworkinthelate1970sonselectionbiasandhiscloselyrelatedworkondummyendogenousvariables Heckman 1978 addressthesameissueofestimatingtreatmenteffectswhenassignmentisnonrandom Heckman sworkonthedummyendogenousvariableproblemandtheselectionmodelcanbeunderstoodasageneralizationofthepropensity scoreapproach Winship Morgan 1999 Inthe1990s Heckmanandhiscolleaguesdevelopeddifference in differencesapproach whichisasignificantcontributiontoPSM Ineconomics theDIDapproachanditsrelatedtechniquesaremoregenerallycallednonexperimentalevaluation oreconometricsofmatching TheCounterfactualFramework Counterfactual whatwouldhavehappenedtothetreatedsubjects hadtheynotreceivedtreatment Thekeyassumptionofthecounterfactualframeworkisthatindividualsselectedintotreatmentandnontreatmentgroupshavepotentialoutcomesinbothstates theoneinwhichtheyareobservedandtheoneinwhichtheyarenotobserved Winship Morgan 1999 Forthetreatedgroup wehaveobservedmeanoutcomeundertheconditionoftreatmentE Y1 W 1 andunobservedmeanoutcomeundertheconditionofnontreatmentE Y0 W 1 Similarly forthenontreatedgroupwehavebothobservedmeanE Y0 W 0 andunobservedmeanE Y1 W 0 TheCounterfactualFramework Continued Underthisframework anevaluationofE Y1 W 1 E Y0 W 0 canbethoughtasaneffortthatusesE Y0 W 0 toestimatethecounterfactualE Y0 W 1 ThecentralinterestoftheevaluationisnotinE Y0 W 0 butinE Y0 W 1 Therealdebateabouttheclassicalexperimentalapproachcentersonthequestion whetherE Y0 W 0 reallyrepresentsE Y0 W 1 FundamentalAssumption Rosenbaum Rubin 1983 Differentversions unconfoundedness ignorabletreatmentassignment Rosenbaum Robin 1983 selectiononobservables Barnow Cain Goldberger 1980 conditionalindependence Lechner1999 2002 and exogeneity Imbens 2004 1 to 1or1 to nMatchNearestneighbormatchingCalipermatchingMahalanobisMahalanobiswithpropensityscoreadded RunLogisticRegression Dependentvariable Y 1 ifparticipate Y 0 otherwise Chooseappropriateconditioning instrumental variables Obtainpropensityscore predictedprobability p orlog 1 p p GeneralProcedure Multivariateanalysisbasedonnewsample 1 to 1or1 to nmatchandthenstratification subclassification KernelorlocallinearweightmatchandthenestimateDifference in differences Heckman Either Or NearestNeighborandCaliperMatching Nearestneighbor ThenonparticipantwiththevalueofPjthatisclosesttoPiisselectedasthematch Caliper Avariationofnearestneighbor Amatchforpersoniisselectedonlyifwhere isapre specifiedtolerance Recommendedcalipersize 25 p1 to 1Nearestneighborwithincaliper Theisacommonpractice 1 to nNearestneighborwithincaliper MahalanobisMetricMatching withorwithoutreplacement Mahalanobiswithoutp score Randomlyorderingsubjects calculatethedistancebetweenthefirstparticipantandallnonparticipants Thedistance d i j canbedefinedbytheMahalanobisdistance whereuandvarevaluesofthematchingvariablesforparticipantiandnonparticipantj andCisthesamplecovariancematrixofthematchingvariablesfromthefullsetofnonparticipants Mahalanobismetricmatchingwithp scoreadded touandv NearestavailableMahalandobismetricmatchingwithincalipersdefinedbythepropensityscore needyourownprogramming Stratification Subclassification Matchingandbivariateanalysisarecombinedintooneprocedure nostep 3multivariateanalysis Groupsampleintofivecategoriesbasedonpropensityscore quintiles Withineachquintile calculatemeanoutcomefortreatedandnontreatedgroups Estimatethemeandifference averagetreatmenteffects forthewholesample i e allfivegroups andvarianceusingthefollowingequations MultivariateAnalysisatStep 3 Wecouldperformanykindofmultivariateanalysisweoriginallywishedtoperformontheunmatcheddata Theseanalysesmayinclude multipleregressiongeneralizedlinearmodelsurvivalanalysisstructuralequationmodelingwithmultiple groupcomparison andhierarchicallinearmodeling HLM Asusual weuseadichotomousvariableindicatingtreatmentversuscontrolinthesemodels VeryUsefulTutorialforRosenbaum Rubin sMatchingMethods D Agostino R B 1998 Propensityscoremethodsforbiasreductioninthecomparisonofatreatmenttoanon randomizedcontrolgroup StatisticsinMedicine17 2265 2281 SoftwarePackages ThereiscurrentlynocommercialsoftwarepackagethatoffersformalprocedureforPSM InSAS LoriParsonsdevelopedseveralMacros e g theGREEDYmacrodoesnearestneighborwithincalipermatching InSPSS Dr JohnPainterofJordanInstitutedevelopedaSPSSmacrotodosimilarworksasGREEDY http sswnt5 sowo unc edu VRC Lectures index htm WehaveinvestigatedseveralcomputingpackagesandfoundthatPSMATCH2 developedbyEdwinLeuvenandBarbaraSianesi 2003 asauser suppliedroutineinSTATA isthemostcomprehensivepackagethatallowsuserstofulfillmosttasksforpropensityscorematching andtheroutineisbeingcontinuouslyimprovedandupdated DemonstrationofRunningSTATA PSMATCH2 Part1 Rosenbaum Rubin sMethods Linktofile Day1c doc ProblemswiththeConventional PriortoHeckman sDID Approaches Equalweightisgiventoeachnonparticipant thoughwithincaliper inconstructingthecounterfactualmean Lossofsamplecasesdueto1 to 1match Whatdoestheresamplerepresent Externalvalidity It sadilemmabetweeninexactmatchandincompletematch whiletryingtomaximizeexactmatches casesmaybeexcludedduetoincompletematching whiletryingtomaximizecases inexactmatchingmayresult Heckman sDifference in DifferencesMatchingEstimator 1 Difference in differencesApplieswheneachparticipantmatchestomultiplenonparticipants Participantiinthesetofcommon support Multiplenonparticipantswhoareinthesetofcommon support matchedtoi Difference Differences in Totalnumberofparticipants Weight seethefollowingslides WeightsW i j distancebetweeniandj canbedeterminedbyusingoneoftwomethods Kernelmatching whereG isakernelfunctionand nisabandwidthparameter Heckman sDifference in DifferencesMatchingEstimator 2 Locallinearweightingfunction lowess Heckman sDifference in DifferencesMatchingEstimator 3 AReviewofNonparametricRegression CurveSmoothingEstimators IamgratefultoJohnFox theauthorofthetwoSagegreenbooksonnonparametricregression 2000 forhisprovisionoftheRcodetoproducetheillustratingexample WhyNonparametric WhyParametricRegressionDoesn tWork Focalx 120 The120thorderedxSaintLucia x 3183y 74 8 Thewindow calledspan contains 5N 95observations TheTask DeterminingtheY valueforaFocalPointX 120 Tricubekernelweights WeightswithintheSpanCanBeDeterminedbytheTricubeKernelFunction TheY valueatFocalX 120 IsaWeightedMean Weightedmean 71 11301 TheNonparametricRegressionLineConnectsAll190AveragedYValues ReviewofKernelFunctions Tricubeisthedefaultkernelinpopularpackages Gaussiannormalkernel Epanechnikovkernel parabolicshapewithsupport 1 1 Butthekernelisnotdifferentiableatz 1 Rectangularkernel acrudemethod LocalLinearRegression Alsoknownaslowessorloess AmoresophisticatedwaytocalculatetheYvalues Insteadofconstructingweightedaverage itaimstoconstructasmoothlocallinearregressionwithestimated 0and 1thatminimizes whereK isakernelfunction typicallytricube TheLocalAverageNowIsPredictedbyaRegressionLine InsteadofaLineParalleltotheX axis AsymptoticPropertiesoflowess Fan 1992 1993 demonstratedadvantagesoflowessovermorestandardkernelestimators Heprovedthatlowesshasnicesamplingpropertiesandhighminimaxefficiency InHeckman sworkspriorto1997 heandhisco authorsusedthekernelweights Butsince1997theyhaveusedlowess Inpracticeit sfairlycomplicatedtoprogramtheasymptoticproperties NosoftwarepackagesprovideestimationoftheS E forlowess Inpractice oneusesS E estimatedbybootstrapping BootstrapStatisticsInference 1 Itallowstheusertomakeinferenceswithoutmakingstrongdistributionalassumptionsandwithouttheneedforanalyticformulasforthesamplingdistribution sparameters Basicidea treatthesampleasifitisthepopulation andapplyMonteCarlosamplingtogenerateanempiricalestimateofthestatistic ssamplingdistribution Thisisdonebydrawingalargenumberof resamples ofsizenfromthisoriginalsamplerandomlywithreplacement AcloselyrelatedideaistheJackknife droponeout Thatis itsystematicallydropsoutsubsetsofthedataoneatatimeandassessesthevariationinthesamplingdistributionofthestatisticsofinterest BootstrapStat