Table of Contents
Preface second editionPreface to first editionIntroductionMultilevel analysisProbability modelsThis bookPrerequisitesNotationMultilevel Theories, Multi-Stage Sampling and Multilevel ModelsDependence as a nuisanceDependence as an interesting phenomenonMacro-level, micro-level, and cross-level relationsGlommaryStatistical Treatment of Clustered DataAggregationDisaggregationThe intraclass correlationWithin-group and between group varianceTesting for group differencesDesign effects in two-stage samplesReliability of aggregated variablesWithin-and between group relationsRegressionsCorrelationsEstimation of within-and between-group correlationsCombination of within-group evidenceGlommaryThe Random Intercept ModelTerminology and notationA regression model: fixed effects onlyVariable intercepts: fixed or random parameters?When to use random coefficient modelsDefinition of the random intercept modelMore explanatory variablesWithin-and between-group regressionsParameter estimation'Estimating' random group effects: posterior meansPosterior confidence intervalsThree-level random intercept modelsGlommaryThe Hierarchical Linear ModelRandom slopesHeteroscedasticityDo not force 01 to be 0!Interpretation of random slope variancesExplanation of random intercepts and slopesCross-level interaction effectsA general formulation of fixed and random partsSpecification of random slope modelsCentering variables with random slopes?EstimationThree or more levelsGlommaryTesting and Model SpecificationTests for fixed parametersMultiparameter tests for fixed effectsDeviance testsMore powerful tests for variance parametersOther tests for parameters in the random partConfidence intervals for parameters in the random partModel specificationWorking upward from level oneJoint consideration of level-one and level-two variablesConcluding remarks on model specificationGlommaryHow Much Does the Model Explain?Explained varianceNegative values of R2?Definition of the proportion of explained variance in two-level modelsExplained variance in three-level modelsExplained variance in models with random slopesComponents of varianceRandom intercept modelsRandom slope modelsGlommaryHeteroscedasticityHeteroscedasticity at level oneLinear variance functionsQuadratic variance functionsHeteroscedasticity at level twoGlommaryMissing DataGeneral issues for missing dataImplications for designMissing values of the dependent variableFull maximum likelihoodImputationThe imputation methodPutting together the multiple resultsMultiple imputations by chained equationsChoice of the imputation modelGlommaryAssumptions of the Hierarchical Linear ModelAssumptions of the hierarchical linear modelFollowing the logic of the hierarchical linear modelInclude contextual effectsCheck whether variables have random effectsExplained varianceSpecification of the fixed partSpecification of the random partTesting for heteroscedasticityWhat to do in case of heteroscedasticityInspection of level-one residualsResiduals at level twoInfluence of level-two unitsMore general distributional assumptionsGlommaryDesigning Multilevel StudiesSome introductory notes on powerEstimating a population meanMeasurement of subjectsEstimating association between variablesCross-level interaction effectsAllocating treatment to groups or individualsExploring the variance structureThe intraclass correlationVariance parametersGlommaryOther Methods and ModelsBayesian inferenceSandwich estimators for standard errorsLatent class modelsGlommaryImperfect HierarchiesA two-level model with a crossed random factorCrossed random effects in three-level modelsMultiple membership modelsMultiple membership multiple classification modelsGlommarySurvey WeightsModel-based and design-based inferenceDescriptive and analytic use of surveysTwo kinds of weightsChoosing between model-based and design-based analysisInclusion probabilities and two-level weightsExploring the informativeness of the sampling designExample: Metacognitive strategies as measured in the PISA studySampling designModel-based analysis of data divided into partsInclusion of weights in the modelHow to assign weights in multilevel modelsAppendix. Matrix expressions for the single-level estimatorsGlommaryLongitudinal DataFixed occasionsThe compound symmetry modelsRandom slopesThe fully multivariate modelMultivariate regression analysisExplained varianceVariable occasion designsPopulations of curvesRandom functionsExplaining the functions 27415.2.4Changing covariatesAutocorrelated residualsGlommaryMultivariate Multilevel ModelsWhy analyze multiple dependent variables simultaneously?The multivariate random intercept modelMultivariate random slope modelsGlommaryDiscrete Dependent VariablesHierarchical generalized linear modelsIntroduction to multilevel logistic regressionHeterogeneous proportionsThe logit function: Log-oddsThe empty modelThe random intercept modelEstimationAggregationFurther topics on multilevel logistic regressionRandom slope modelRepresentation as a threshold modelResidual intraclass correlation coefficientExplained varianceConsequences of adding effects to the modelOrdered categorical variablesMultilevel event history analysisMultilevel Poisson regressionGlommarySoftwareSpecial software for multilevel modelingHLMMLwi NThe MIXOR suite and Super MixModules in general-purpose software packagesSAS procedures VARCOMP, MIXED, GLIMMIX, and NLMIXEDRStataSPSS, commands VARCOMP and MIXEDOther multilevel softwarePin TOptimal DesignMLPow SimMplusLatent GoldREALCOMWin BUGSReferencesIndex