class13 Regression Analysis of Correlated Data-new-f2008

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1、TheRegressionAnalysisofCorrelatedDataTherearemanysituationsthatresultinsamplesthatarenotmadeupofindependentobservations•Familydata:Wecanexpectthatsubjectsinthesamefamilywillhaveobservationsthataremorealikewhencomparedtoeachotherthanwhencomparedtosubjectsi

2、notherfamilies.•Datacollectedusingnon-randomsampling:Whenusingasamplingschemethatselectsseveralhospitalsfromwhichsubjectswillberecruited,subjectsatthesamehospitalwillshareunmeasuredcharacteristicsthatwouldnothappenifsubjectswereselectedrandomlyfromthegene

3、ralpopulation.•Repeatedmeasures:Whentakingrepeatedmeasurementsfromsubjects,observationsthatarefromthesamesubjectwilltendtobemorealikethanwhencomparedtoothersubjectsobservations.Repeatedobservationscloserintimefromthesamesubjectmayalsobemorealikethanthosef

4、urtherapartintime.2ConsequencesofNon-IndependentDataConsiderthisexperiment:•Youattendaconventionforidenticaltripletsthathas1,000setsofidenticaltriplets.•Youdecideyouhavetimetotake1,000systolicbloodpressuremeasurements.Youcaneither:1.Collectbloodpressuresf

5、romallmembersof333-1/3setsoftripletsor,2.Takeonemeasurefromeachofthe1,000sets.IfyouwantaproperestimateofSBPattheconvention,areyoubetteroffdoing1or2?•Ifmembersofatriplettendtohavesimilarbloodpressures,yougetlittleadditionalinformationbymeasuringmorethanone

6、memberofasibship.•Thetotalinformationcontentofyourdatawillbereducedifyoudon’thaveindependentobservations.•Thestandarderrorsonyourestimateswillbetoosmallifyoudon’taccountforthecorrelations–yourdataisnotasgoodasyouthink!3Situation#2:SleepHoursinMenandWomen•

7、Youaretestingthehypothesisthatmothersandfathersofnewbornswillgetsignificantlydifferenthoursofsleep,whereyoubelievethatmenwillsleepmorethanwomen.•Youcandothestudytwoways:1.Youcollect50couplesandcalculatethedifferenceinsleephoursbetweenthemotherandfatherofa

8、newborn.Isthisdifferencesignificantlydifferentfromzero?[pairedt-testwith50pairs].2.Youaccumulate50mothersand50fathersofnewborns,withnoattempttorecruitcouples.Youthencalculatethemeannumberofhoursofsleepinmothersandin