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1、Chapter10CounterfactualCausalAnalysisandNonlinearProbabilityModelsRichardBreenandKristianBerntKarlsonAbstractNonlinearprobabilitymodels,suchaslogitsandprobitsforbinarydependentvariables,theorderedlogitandorderedprobitforordinaldependentvariablesandthemultinomiallogit,
2、togetherwithlog-linearmodelsforcontingencytables,havebecomewidelyusedbysocialscientistsinthepast30years.Inthischapter,weshowthattheidentiÞcationandestimationofcausaleffectsusingthesemodelspresentseverechallenges,overandabovethoseusuallyencounteredinidentifyingcausalef
3、fectsinalinearsetting.ThesechallengesarederivedfromthelackofseparateidentiÞcationofthemeanandvarianceinthesemodels.Weshowtheirimpactinexperimentalandobservationalstudies,andweinvestigatetheproblemsthatariseintheuseofstandardapproachestothecausalanalysisofnonexperiment
4、aldata,suchaspropensityscores,instrumentalvariables,andcontrolfunctions.Naiveuseoftheseapproacheswithnonlinearprobabilitymodelswillyieldbiasedestimatesofcausaleffects,thoughtheestimateswillbealowerboundofthetruecausaleffectandwillhavethecorrectsign.Weshowthatthetechni
5、queofY-standardizationbringstheparametersofnonlinearprobabilitymodelsonascalethatwecanmeaningfullyinterpretbutcannotmeasure.Othertechniques,suchasaveragepartialeffects,canyieldcausaleffectsontheprobabilityscale,but,inthiscase,thelinearprobabilitymodelprovidesasimplean
6、deffectivealternative.IntroductionManyoftheoutcomesencounteredinsocialresearcharecategorical,ordinal,orcounts.Severalmodelshavebeendevelopedtodealwithdataofthesesorts:theyincludelog-linearmodelsforcontingencytables;logitandprobitmodelsforbinarydependentvariables;cumul
7、ativeprobabilitymodels,suchastheorderedlogitandorderedprobit,forordinaldependentvariables;andthemultinomiallogitforunorderedpolytomouscategoricaloutcomes.AlthoughmanysocialscientistsbelievethatcoefÞcientsfromthesemodelscanbeinterpretedinthesamewayascoefÞcientsfromline
8、armodels,thisisnotso.Innonlinearprobabilitymodelslikethelogit,probit,orderedlogit,R.Breen()DepartmentofSociology,YaleUniver
