chapter7 - Multiple Regression Analysis with Qualitative Information (1&amp#215;1).pdf

《chapter7 - Multiple Regression Analysis with Qualitative Information (1&amp#215;1).pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、Chapter7MultipleRegressionAnalysiswithQualitativeInformationBinary(orDummy)Variables1MainContents本章主要内容BasicsofDummyIndependentVariable虚拟变量作为解释变量进入模型的一般方式MultipleCategories多个类别的情形InteractionInvolvingDummies虚拟变量的交互项应Goodness-of-FitandSelectionofRe

2、gressors拟合优度和回归元的选择ABinaryDependentVariable被解释变量是二值变量2虚拟变量进入模型的一般方式：加法两个类别/多个类别情形3DummyVariable:Definition虚拟变量定义Adummyvariableisavariablethattakesonthevalue1or0,alsocalledasabinaryvariable.虚拟变量也称为二值变量，取值为0或者14DummyVariable:InterceptShift虚拟变量：体现截距的不

3、同---加法方式引进模型Considerasimplemodelwithonecontinuousvariable(x)andonedummy(d):将虚拟变量d加入模型：ydxu001Thiscanbeinterpretedasaninterceptshift:可以看作截距的变化：Ifd=0,theny=+x+u01Ifd=1,theny=(+)+x+u001Thecaseofd=0isthebasegroup通常d=0的情形作为基准组Thedifferenceint

4、heinterceptsis不同情形下的截距为：0Eyd1,xEyd0,x注意到Eyd1,x=001++xEyd;0,x=01+xdueonlytothequalitativecharacteristic.5DummyVariable:InterceptShift虚拟变量：截距的变化yy=(0+0)+1xd=1slope=1{d=00y=+x01}0x6DummyVariable:DummyTrapProblem注意虚拟变量陷阱Questi

5、on:Canwespecifythefollowingmodel:yfemalemalexu00111,ifindividualisfemalefemale0,otherwise1,ifindividualismalemale0,otherwise可以如此设定虚拟变量并建立模型吗？No!Thetwodummiesareperfectlinear:female+male=1.不可以！female+male=1，解释变量完全共线！Onlyuseoneofthetw

6、odummiesinthemodelorusethetwodummiesinthemodelwithoutanintercept如果一定要包含这两个虚拟变量，则模型去掉常数项。7DummiesforMultipleCategories模型中包含多重类别因素情形（1）Example:logwage00female1married1educuTheimportantlimitationofthismodelisthatthemarriagepremiumisassumedt

7、obethesameformenandwomen.局限：该模型隐含婚姻对工资的影响，无论男女都是相同的。Now,Fourgroups:marriedmen,marriedwomen,singlemen,andsinglewomen.考虑四个组别，定义四个虚拟变量：logwage00marrmale1marrfem2singfem1educuHere,dummyvariablesformultiplecategoriesareused.Thebasegroupissin

8、glemensuchthatthedummytrapisavoided.四个类别，但模型中加入三个虚拟变量，基准组为单身男性。8模型系数含义（一）logwagemarrmalemarrfemsingfemeducu00121Elogwage单身男性,edu,01educElogwage已婚男性,edu,001educElogwage已婚女性,edu,01