英国诺丁汉大学讲义如何估计随机效应模型stata

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1、MCMCEstimationforRandomEffectModelling–TheMLwiNexperienceDrWilliamJ.BrowneSchoolofMathematicalSciencesUniversityofNottinghamContentsRandomeffectmodelling,MCMCandMLwiN.Methodscomparison–Guatemalanchildhealthexample.ExtendibilityofMCMCalgorithms:Crossclas

2、sifiedandmultiplemembershipmodels.ArtificialinseminationandDanishchickenexamples.FurtherExtensions.RandomeffectmodelsModelsthataccountfortheunderlyingstructureinthedataset.Originallydevelopedfornestedstructures(multilevelmodels),forexampleineducation,pu

3、pilsnestedwithinschools.Anextensionoflinearmodellingwiththeinclusionofrandomeffects.Atypical2-levelmodelisHereiindexespupilsandjindexesschools.MLwiNSoftwarepackagedesignedspecificallyforfittingmultilevelmodels.DevelopedbyateamledbyHarveyGoldsteinandJonR

4、asbashattheInstituteofEducationinLondonoverpast15yearsorso.EarlierincarnationsML2,ML3,MLN.Originallycontained‘classical’IGLSestimationmethodsforfittingmodels.MLwiNlaunchedin1998alsoincludedMCMCestimation.MyroleinteamwasasdeveloperofMCMCfunctionalityinML

5、wiNduring4.5yearsattheIOE.EstimationMethodsforMultilevelModelsDuetoadditionalrandomeffectsnosimplematrixformulaeexistforfindingestimatesinmultilevelmodels.Twoalternativeapproachesexist:Iterativealgorithmse.g.IGLS,RIGLS,EMinHLMthatalternatebetweenestimat

6、ingfixedandrandomeffectsuntilconvergence.CanproduceMLandREMLestimates.Simulation-basedBayesianmethodse.g.MCMCthatattempttodrawsamplesfromtheposteriordistributionofthemodel.MCMCAlgorithmConsiderthe2-levelmodelMCMCalgorithmsworkinaBayesianframeworkandsowe

7、needtoaddpriordistributionsfortheunknownparameters.Herethereare4setsofunknownparameters:WewilladdpriordistributionsMCMCAlgorithm(2)Thealgorithmforthismodeltheninvolvessimulatinginturnfromthe4setsofconditionaldistributions.SuchanalgorithmisknownasGibbsSa

8、mpling.MLwiNusesGibbssamplingforallnormalresponsemodels.Firstlywesetstartingvaluesforeachgroupofunknownparameters,Thensamplefromthefollowingconditionaldistributions,firstlyToget.MCMCAlgorithm(3)Wenextsamplefromtoget,thentoget,the