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1、JOURNALOFAPPLIEDECONOMETRICSJ.Appl.Econ.15:447±470(2000)MIXEDMNLMODELSFORDISCRETERESPONSEDANIELMCFADDEN*ANDKENNETHTRAINDepartmentofEconomics,UniversityofCalifornia,Berkeley,CA,94720-3880,USASUMMARYThispaperconsidersmixed,orrandomcoecients,multinomiallogit(MMNL)modelsfordiscreterespon
2、se,andestablishesthefollowingresults.Undermildregularityconditions,anydiscretechoicemodelderivedfromrandomutilitymaximizationhaschoiceprobabilitiesthatcanbeapproximatedascloselyasonepleasesbyaMMNLmodel.PracticalestimationofaparametricmixingfamilycanbecarriedoutbyMaximumSimulatedLikel
3、ihoodEstimationorMethodofSimulatedMoments,andeasilycomputedinstrumentsareprovidedthatmakethelatterprocedurefairlyecient.Theadequacyofamixingspeci®cationcanbetestedsimplyasanomittedvariabletestwithappropriatelyde®nedarti®cialvariables.Anapplicationtoaproblemofdemandforalternativevehic
4、lesshowsthatMMNLprovidesa¯exibleandcomputationallypracticalapproachtodiscreteresponseanalysis.Copyright#2000JohnWiley&Sons,Ltd.1.INTRODUCTIONDe®neamixedmultinomiallogit(MMNL)modelasaMNLmodelwithrandomcoecientsadrawnfromacumulativedistributionfunctionG(a;y):ZXxaxaP…ijx;y†ˆL…i;x;a†G…d
5、a;y†withL…i;x;a†ˆei=ej…1†CCCj2CInthissetup,Cˆf1;...;Jgisthechoiceset;thexare1Kvectorsoffunctionsofobservediattributesofalternativeiandobservedcharacteristicsofthedecisionmaker,withxˆ…x;...;x†;aisaK1vectorofrandomparameters;L…i;x;a†isaMNLmodelfor1JCthechoicesetC;andyisavectorofdeepp
6、arametersofthemixingdistributionG.TherandomparametersamaybeinterpretedasarisingfromtasteheterogeneityinapopulationofMNLdecisionmakers.Ifthexcontainalternative-speci®cvariables,thenthecorrespondingicomponentsofacanbetreatedasalternative-speci®crandomeects.Alternately,themodelmaysimply
7、beinterpretedasa¯exibleapproximationtochoiceprobabilitiesgeneratedbyarandomutilitymodel.ThemixingdistributionGmaycomefromacontinuousparametricfamily,suchasmultivariatenormalorlognormal,oritmayhavea®nitesupport.WhenGhas®nitesupport,MMNLmodelsarealsocalledlatentclassmodels.Equation(1)d
8、escribesasin
