Multinomial and Ordered Response Models.pdf

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1、MultinomialandOrderedResponseModelsPhDEconometricsWeitanHanqingAdvancedInstituteofEconomicsandFinanceRenminUniversityofChinaWeiTan(RUC)MultinomialandOrderedResponseModels1/28MultinomialLogitLetydenotearandomvariabletakingonthevaluesf0;1;


;JgforJapositiveinteger,an

2、dxa1Kvectorwith…rst-elementunity.Themultinomiallogit(MNL)modelhasresponseprobabilities:"#XJP(y=jjx)=exp(xj)=1+exp(xh);j=1;


;J(1)h=1wherejisK1,j=1;


;J.Becausetheresponseprobabilitymustsumtounity,"#XJP(y=0jx)=1=1+exp(xh)h=1WhenJ=1,1istheK1vectorofunknownparamet

3、ers,andwegetthebinarylogitmodel.WeiTan(RUC)MultinomialandOrderedResponseModels2/28MultinomialLogitThepartiale¤ectsforMNLmodelarecomplicated.Forcontinuousxk,wecanwrite("#)XJ@P(y=jjx)=P(y=jjx)jk