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1、CHAPTER30REGRESSIONESTIMATIONINTHEPRESENCEOFMEASUREMENTERRORWayneA.FullerIowaStateUniversity30.1INTRODUCTIONRegressionisatechniqueoftenusedintheanalysisofsurveydata.Theclassicalregressionmodelisyt=x't?+qt(30.1)2wheretheqtareindependent(0,σ)randomvariablesindepend
2、entofx;foralltand;',x,isaA:-dimensionalcolumnvectorofexplanatoryvariablesandβistheunknownparametervector.Surveydatatypicallyviolatetheclassicalmodelintwoimportantways.Ifthesurveyisaclusteredsampleitisnolongerreasonabletoassumethattheqtwithinaclusterareindependent
3、.Thisfacthasbeenrecognizedforsometime.See,forexample,Frankel(1971),Fuller(1975),andFullerandHidiroglou(1978).Furthermore,computerpackageshavebeendevelopedtocomputeregressioncoefficientsandthestandarderrorsofregressioncoefficientsforcomplexsurveydata.Examplesofsuc
4、hprogramsincludeSUPERCARP,PCCARP,andSUDAAN.Thesecondimportantwayinwhichsurveydataviolatethemodelisthatonedoesnotobserve(yt,xO-Ratheroneobserves(y?XD=(*,xi)+(u>i.uDwhere(wt,uj)isthevectorofmeasurementerror.Insurveysampling,theThisresearchwaspartlysupportedbyJointS
5、tatisticalAgreementJ.S.A90-7withtheU.S.BureauoftheCensus.IthankJosephCrooeforthecomputationsofthedesignsectionandforthecomputationsoftheillustration.MeasurementErrorsinSurveys.EditedbyBiemer,Groves,Lyberg,Mathiowetz,andSudman.Copyright?1991byJohnWiley&Song,Inc.IS
6、BN:0-471-53405-6618REGRESSIONESTIMATIONWITHMEASUREMENTERRORmeasurementerrorisoftencalledresponseerrorbecauseaprimarysourceoferroristhefailureofrespondentstogivethesameanswertoarepeatedquestion.Thatsurveydataaresubjecttomeasurementerrorisuniformlyrecognizedbytheco
7、mmunityofsurveysamplers.AnearlydescriptionoftheeffectofmeasurementerroronestimatesofchangeisthatofBershad(1967).ExamplesoftheincorporationofestimatesofmeasurementerrorvariancesintoanalysesofsurveydataincludeWarren,etal.(1974),Rodgers(1989a),ChuaandFuller(1987),Po
8、terbaandSummers(1985),AbowdandZellner(1985),andnumerousarticlesinpsychologyandsociologyjournals.Despitethislistofreferences,itseemsfairtosaythatthefractionofre
