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1、MultilevelModeling:1WhenandWhyJ.HoxUniversityofAmsterdam&UtrechtUniversityAmsterdam/Utrecht,theNetherlandsAbstract:Multilevelmodelshavebecomepopularfortheanalysisofavarietyofproblems,goingbeyondtheclassicalindividuals-within-groupsapplications.Thischapter
2、givesabriefsummaryofthereasonsforusingmultilevelmodels,andprovidesexampleswhythesereasonsareindeedvalidreasons.Next,recent(simulation)researchisreviewedontherobustnessandpoweroftheusualestimationprocedureswithvaryingsamplesizes.1Whymultileveldataneedmulti
3、levelmodelsMultilevelmodelsaremodelsspecificallygearedtowardthestatisticalanalysisofdatathathaveahierarchicalorclusteredstructure.Suchdataariseroutinelyinvariousfields,forinstanceineducationalresearch,wherepupilsarenestedwithinschools,familystudieswithchi
4、ldrennestedwithinfamilies,medicalresearchwithpatientsnestedwithinphysiciansorhospitals,andbiologicalresearch,forinstancetheanalysisofdentalanomalieswithteethnestedwithindifferentpersons'mouths.Clustereddatamayalsoariseasaresultofthespecificresearchdesign.
5、Forinstance,inlargescalesurveyresearchthedatacollectionisusually,foreconomicreasons,organizedinsomesortofmultistagesamplingdesignthatresultsinclusteredorstratifieddesign.Anotherexamplearelongitudinaldesigns;onewayofviewinglongitudinaldataisasaseriesofrepe
6、atedmeasurementsnestedwithinindividualsubjects.Olderapproachestotheanalysisofmultileveldata,suchasreviewedinHuetnnerandVandenEeden(1982),tendtosimplyignorethequestion,andperformtheanalysisbydisaggregatingalldatatothelowestlevelandsubsequentlyapplyingstand
7、ardanalysismethods.Theproblemscreatedbythisapproachwererecognized(e.g.,Burstein,1980),butremainedstatisticallyintractable.Themagnitudeofthestatisticalproblemcanbeillustratedbyasimpleexamplefromsamplesurveys.Surveystatisticianshavelongknownthattheextendtow
8、hichthesamplesareclusteredaffectsthesamplingvariance.Inhisclassicwork,Kish(1965)providesadetailedexaminationoftheeffectofclustersamplingonsampling1Pp.147-154in:I.Balderjahn,R.Mathar&M.Schader(Eds.).Classification,da
