missing data measurement errors and outliers

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1、CHAPTER3MissingData,MeasurementErrors,andOutliers3.1IntroductionInlongitudinalstudies,observeddataareoftenincompletesinceitisdifculttoobservealldataforeveryvariableateachmeasurementtime,especiallyifthestudieslastalongtime.Incompletedataarealsocommoninothertypesofstu

2、dies,includingcross-sectionalstudies.Inmanystudies,datamayalsobecensoredormis-measured.Specically,thefollowingproblemsarecommoninpractice:(i)missingdata:thedataarecompletelymissing,(ii)censoreddata:thetruedataarenotobservedbuttheyareknowntobeincertainranges,(iii)mis

3、-measureddata:thetruedataarenotobservedbuttheirmis-measuredver-sionsareobserved,(iv)outliers:theobserveddatamayormaynotbethetruevaluesbuttheyareinconsistentwithmajorityoftheobserveddata.Forlastthreecases,althoughthetruedatamaynotbeobserved,partialinformationisavailab

4、leforthetruevaluessotheymayalsobecalledincompletedata.Toavoidconfusion,weusethetermmissingdatatorefertodatathatarecom-pletelymissingandusethetermincompletedatatorefertothemoregeneralcases,i.e.,oneoftheabovefourcases.Inthischapter,wereviewsomecom-monlyusedgeneralmetho

5、dsforincompletedataproblems.Inthepresenceofmissingdata,itisimportanttochooseappropriatemethodsfordataanalysissincesimpleornaivemethodsmayleadtobiasedresults.Forexample,ifasubjectwithdrawsfromastudyduetoconditionsrelatedtothestudy,discardingorignoringthemissingdatawil

6、lleadtobiasedanalyses.Thus,oneshouldrstcheckpossiblereasonsofmissingdataorhowthedataaremissing,i.e.,thepossiblemissingdatamechanisms.Choicesofappropriatemethodsfordataanalysisarethenbasedonthemissingdatamechanisms.Inpracticeitisoftendifculttodeterminethemissingdata

7、mechanisms,sincethedataanalystmaynotbetheonewhocollectsthedata.Inthiscase,onemayanalyzethedataunderseveralplausiblemissingdatamechanismsandthencheckiftheresultsdiffersubstantially.Thisiscalledsensitivityanalysis.9798MIXEDEFFECTSMODELSFORCOMPLEXDATACensoreddatamaybevi

8、ewedasaspecialtypeofmissingdatainwhichthecensoredvaluesareunobservedbutareknowntobeincertainranges.Censor-ingarisesinstudieswherece