二元离散选择模型案例

第七章二元离散选择模型案例一、在一次选举中，由于候选人对高收入者有利，因此收入成为每一个投票者表示同意或反对的最要紧阻碍因素。以投票者的态度（y）作为被说明变量，以投票者的月收入（x）作为说明变量成立模型，同意者其观测值为1反对者其观测值为0样本数据见表。原始模型为：y"+Bx+卩。利用Probit二元离i ii散选择模型估量参数。表样本观测值序号XY序号XY序号XY110001111000212100122000121200022220013300013130012323001440001414000242400155000151500125250016600016160002626001770001717001272700188000181800028280019900019190012929001101000020200013030001估量进程如下:EquationEstzLnationSpeciticatiunOt-*ioilsEquatiqilEquatiqil昌f启ci c01io口DeperLilentv==Lt~iaLlefoilowedbylistotrH：gi_esEorsJiiLilFDLtemiE,匸IF：qtlr咒卫1iciitequatiDnlikeEstimatiEstimatioilsettingsMethod：LS一LeastS&e(JILS:aiLilMJIA.'ILS_LeastSipi：iree(MTS：±tl»1AJJJA)TSLS-Twu_5tag&Least 汕(TSBL5andAE-llAJGMM一Generalized.NethodofMcmentsAJlCH二kutury蹴色空辽旦匸g足Qjfjj?卫里卫g1gyg韭edazticity_ElITATlY一T!in：=Lt_ychcice ogit】卩广匸上心JextreniHijMEFJEli一izirder&iichuiceCEITSuFlEIl一CeiLEore-1ortrijnciteddata(,tobit,)CLltrHT一IiLtegercoimtdataiiii输入变量名，选择Probit参数估量。

取得如下输出结果：DeperidentVariable:YMethod:ML-BinaryProbit(Quadratichillclimbing)Date:07/08AJ8Time:15:57Sample:130Includedobsen/atioris:30Convergenceachievedafter5iterationsCovariaricematrixcom卩山日山usingsecondderivativesVariableCoefficientStd.Errorz-StatisticProL.C-47533961.392117 -2.5124750.0120*0.0030670.001192 2.5731210.0101Meandependentvar0.500000S.D.dependentvar0.50B543S.E.ofregression0.274450Akaikeinfacriterion0.539743Sumsquaredresid2.109040Schwarzcriterion0.633156Loglikelihood-6.096147Hannan-Quinncriter.0.569627Restr.loglikelihood-2079442Avg.loglikelihood■0.203205LRstatistic(1df)29.39654McFaddenR-squared0.706037ProbabilityfLRstat)5.9OE-O0ObswithDep=015Totalobs30ObswithDep=115可是作为估量对象的不是原始模型，而是如下结果：YF二1-@CONRM[—(—4.7539+0.003067*X)]能够取得不同X值下的Y选择1的概率。例如，当X=600时，査标准正态散布表，对应于的积存正态散布为；于是，Y的预测值YF==，即对应于该个人，投同意票的概率为。二、某商业银行从历史贷款客户中随机抽取78个样本，依照涉及的指标体系别离计算它们

的“商业信誉支持度”（XY）和“市场竞争地位品级”（SC）,对它们贷款的结果（JG）采纳二元离散变量，1表示贷款成功，0表示贷款失败。样本观测值见表。目的是研究JG与XY、SC之间的关系，并为正确贷款决策提供支持。表样本观测值JGXYSCJGFJGXYSCJGFJGXYSCJG20054-100599-2009600142210100-201-80104200160-200375-2011821046-20042-10801080-2015211-5010133-200172-200326200350-101-8010261101230089-201-2-1060-200128-20014-2070-10160112201-8010150-100113100400-2015421142107200028-2015720120-1012500146001401123011501135111401026-212611049-10089-20115-1014-11511069-1006101-9-1101071014021141112911030-20054-2012110112-10132111371078-200540053-1010010131-200194000131-2011501估量进程如下：

输入变量名，选择Logit参数估量。EquationEatiKationEpeciEicationUptioilsEquationEjecific：±tionEin：输入变量名，选择Logit参数估量。EquationEatiKationEpeciEicationUptioilsEquationEjecific：±tionEin：』■乎 v：=d-iatilt dbylistofJgcKJTECBinaryestimation Fi"obiOEji'giE^trernev：aluMethod:SIMA^YBinarychoice(legit,probit,estremavalue)职消Simple：1T8职消确走取得如下输出结果:

DependentVariable:JGMethod:ML-BinaryLogit(Quadratichillclimbing)Date:07^08^18Time:16:10Sample:178Includedotiservations:78Corivergenceachievedafler9iterationsCovariancematrixcomputedusingsecondderivativesVariableCoefficientStd.Errorz-StatisticProb.C16.1142614.5636S 1.1064690.2GS5XY-0.4650350.431764 -1.07705B0.2B15SC9.3799038.712527 1.0766000.2B17Meandependentvar0.410256S.D.dependentvar0.495064S.E.ofregression0.091187Akaikeinfocriterion0.120325Sunnsquaredresid0.623629Schwarzcriterion0.21096BLoglikelihood-1.692674Hannan-Quinncriter.0.156611Restr.loglikelihood-52.B0224Avg.laglikelihood-0.021701LRstatistic(2dfl102.2191McFaddenR-squared0.967943Probability(LRstat)o.oooaooObswithDep=046Totalobs78ObswithDep=132用回归方程表示如下：JGF=1-@CONRM[—（16.11—0.465035*XY+9.379903*SC）]该方程表示，当XY和SC已知时，带入方程，能够计算贷款成功的概率JGF。3、某研究所1999年50名硕士考生的入学考试总分数（SCORE）及录取情形见表5。考生考试总分数用SCORE表示，Y为录取状态，D1为表示应届生与往届生的虚拟变量。表50名硕士考生的入学考试总分数（SCORE）及录取状况数据表序数YSCORED1序数YSCORED1114011260347121401027034713139212803441413870290339151384130033806137903103381713780320336181378033033409137613403321101371035033211113620360332112136213703311131361138033011403591390328115035814003281

16135614103281170356142032111803551430321119035414403181200354045031802103531460316122035004703080230349048030812403490490304025034815003031概念如下:1,录取 rf1,应届生0,未录取’ [o,非应届生加入D1变量的目的是想考察考生为应届生或往届生是不是也对录取产生阻碍。考生录取状态（Y）与考试总分数（SCORE）的散点图如以下图所示：由于变量Y只有两种状态，因此应该成立二元选择模型进程如下：EquationEstiBation选择BINARY选择BINARY（二元）估量方式，选择logit模型EquationEstinationSpecificationOptionsycecore>11ElustionspecificationEirL：=d'7亘色EquationEstinationSpecificationOptionsycecore>11ElustionspecificationEirL：=d'7亘色pundentv：=±'i41.11f^11bylist■-fbinary已stimation ■:Frobi(*)LugitC_.：,Extreme卩口口Method：BINAJ^T-BiiL：±r7chuice(logit,.probit._extreme犷£1口自；1VSiiniply：150确定 取消取得如下输出结果:DependentVariable:YMethod:ML-BinaryLogit(Quadratichillclimhing)Date:06/29/08Time:22:28Sample:150Includedobservations:50Convergenceachievedafter8iterationsCovariancematrixcomputedusingsecondderivativesVariableCoefficientStd.Errorz-StatisticProb.C-242.4576124.5182 -1.9471650.0515SCORE0.G770610.34S03G 1.9453800.0517D1-0.4766052.934586 -0.1596090.0731M已日nHe卩已nd已ntvar0.200000S.D.dep已nd巳ntvar0.453557S.E.ofregr已swiori0.163168Akaik巳infocrit已「in门0.279179Sumsquaredresid1.2513165匚hwarzcriterion0.393901Loglikelihood-3.979482Hannan-Quinncriter.0.322866Restr.loglikelihood-29.64767Avg.laglikelihood-0.079590LRstatistic(2df)51.33637McFaddenR-squared0.665774ProbabilityfLRstat)7.12E-12ObswithDep=036Totalobs50ObswithDep=114由D1的相伴概率能够看出，D1的参数没有显著性，说明考生的应届、非应届特点对录取与否无显著性阻碍。从模型中剔除D1，从头估量。结果如下：DependentVariable:YMethod:ML-BinaryLogit(Quadratichillclimbing)Date:06/29/08Time:22:31Sample:150Includedobservations:50Corivergenceachievedafter7iterationsCovariancematrixcomputedusingsecondderivativesVariableCoefficientStd.Error z-StatisticProb.C-243.7362125.5675 -1.9412320.0522SCORE0.6794410.350495 1.9385190.0526Meandependentvar，0.200000S.D.dependentyar0.453557S.E.ofregression0.162405.Akaikeinfocriterion0.239693Sumsquaredresid1.266017Schwarzcri