class13 Regression Analysis of Correlated Data-new-f2008

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1、TheRegressionAnalysisofCorrelatedDataTherearemanysituationsthatresultinsamplesthatarenotmadeupofindependentobservations•Familydata:Wecanexpectthatsubjectsinthesamefamilywillhaveobservationsthataremorealikewhencomparedtoeachotherthanwhencomparedtosubjectsinotherfamilies.•Datac

2、ollectedusingnon-randomsampling:Whenusingasamplingschemethatselectsseveralhospitalsfromwhichsubjectswillberecruited,subjectsatthesamehospitalwillshareunmeasuredcharacteristicsthatwouldnothappenifsubjectswereselectedrandomlyfromthegeneralpopulation.•Repeatedmeasures:Whentaking

3、repeatedmeasurementsfromsubjects,observationsthatarefromthesamesubjectwilltendtobemorealikethanwhencomparedtoothersubjectsobservations.Repeatedobservationscloserintimefromthesamesubjectmayalsobemorealikethanthosefurtherapartintime.2ConsequencesofNon-IndependentDataConsiderthi

4、sexperiment:•Youattendaconventionforidenticaltripletsthathas1,000setsofidenticaltriplets.•Youdecideyouhavetimetotake1,000systolicbloodpressuremeasurements.Youcaneither:1.Collectbloodpressuresfromallmembersof333-1/3setsoftripletsor,2.Takeonemeasurefromeachofthe1,000sets.Ifyouw

5、antaproperestimateofSBPattheconvention,areyoubetteroffdoing1or2?•Ifmembersofatriplettendtohavesimilarbloodpressures,yougetlittleadditionalinformationbymeasuringmorethanonememberofasibship.•Thetotalinformationcontentofyourdatawillbereducedifyoudon’thaveindependentobservations.

6、•Thestandarderrorsonyourestimateswillbetoosmallifyoudon’taccountforthecorrelations–yourdataisnotasgoodasyouthink!3Situation#2:SleepHoursinMenandWomen•Youaretestingthehypothesisthatmothersandfathersofnewbornswillgetsignificantlydifferenthoursofsleep,whereyoubelievethatmenwills

7、leepmorethanwomen.•Youcandothestudytwoways:1.Youcollect50couplesandcalculatethedifferenceinsleephoursbetweenthemotherandfatherofanewborn.Isthisdifferencesignificantlydifferentfromzero?[pairedt-testwith50pairs].2.Youaccumulate50mothersand50fathersofnewborns,withnoattempttorecr

8、uitcouples.Youthencalculatethemeannumberofhoursofsleepinmothersandin