Multilevel Analysis: An Introduction To Basic And Advanced Multilevel Modeling

Title Page
Copyright Page
Contents
Preface to the Second Edition
Preface to the First Edition
1 Introduction
	1.1 Multilevel analysis
		1.1.1 Probability models
	1.2 This book
		1.2.1 Prerequisites
		1.2.2 Notation
2 Multilevel Theories, Multistage Sampling, and Multilevel Models
	2.1 Dependence as a nuisance
	2.2 Dependence as an interesting phenomenon
	2.3 Macro-level, micro-level, and cross-level relations
	2.4 Glommary
3 Statistical Treatment of Clustered Data
	3.1 Aggregation
	3.2 Disaggregation
	3.3 The intraclass correlation
		3.3.1 Within-group and between-group variance
		3.3.2 Testing for group differences
	3.4 Design effects in two-stage samples
	3.5 Reliability of aggregated variables
	3.6 Within- and between-group relations
		3.6.1 Regressions
		3.6.2 Correlations
		3.6.3 Estimation of within- and between-group correlations
	3.7 Combination of within-group evidence
	3.8 Glommary
4 The Random Intercept Model
	4.1 Terminology and notation
	4.2 A regression model: fixed effects only
	4.3 Variable intercepts: fixed or random parameters?
		4.3.1 When to use random coefficient models
	4.4 Definition of the random intercept model
	4.5 More explanatory variables
	4.6 Within- and between-group regressions
	4.7 Parameter estimation
	4.8 ‘Estimating’ random group effects: posterior means
		4.8.1 Posterior confidence intervals
	4.9 Three-level random intercept models
	4.10 Glommary
5 The Hierarchical Linear Model
	5.1 Random slopes
		5.1.1 Heteroscedasticity
		5.1.2 Do not force τ01 to be 0!
		5.1.3 Interpretation of random slope variances
	5.2 Explanation of random intercepts and slopes
		5.2.1 Cross-level interaction effects
		5.2.2 A general formulation of fixed and random parts
	5.3 Specification of random slope models
		5.3.1 Centering variables with random slopes?
	5.4 Estimation
	5.5 Three or more levels
	5.6 Glommary
6 Testing and Model Specification
	6.1 Tests for fixed parameters
		6.1.1 Multiparameter tests for fixed effects
	6.2 Deviance tests
		6.2.1 More powerful tests for variance parameters
	6.3 Other tests for parameters in the random part
		6.3.1 Confidence intervals for parameters in the random part
	6.4 Model specification
		6.4.1 Working upward from level one
		6.4.2 Joint consideration of level-one and level-two variables
		6.4.3 Concluding remarks on model specification
	6.5 Glommary
7 How Much Does the Model Explain?
	7.1 Explained variance
		7.1.1 Negative values of R2?
		7.1.2 Definitions of the proportion of explained variance in two-level models
		7.1.3 Explained variance in three-level models
		7.1.4 Explained variance in models with random slopes
	7.2 Components of variance
		7.2.1 Random intercept models
		7.2.2 Random slope models
	7.3 Glommary
8 Heteroscedasticity
	8.1 Heteroscedasticity at level one
		8.1.1 Linear variance functions
		8.1.2 Quadratic variance functions
	8.2 Heteroscedasticity at level two
	8.3 Glommary
9 Missing Data
	9.1 General issues for missing data
		9.1.1 Implications for design
	9.2 Missing values of the dependent variable
	9.3 Full maximum likelihood
	9.4 Imputation
		9.4.1 The imputation method
		9.4.2 Putting together the multiple results
	9.5 Multiple imputations by chained equations
	9.6 Choice of the imputation model
	9.7 Glommary
10 Assumptions of the Hierarchical Linear Model
	10.1 Assumptions of the hierarchical linear model
	10.2 Following the logic of the hierarchical linear model
		10.2.1 Include contextual effects
		10.2.2 Check whether variables have random effects
		10.2.3 Explained variance
	10.3 Specification of the fixed part
	10.4 Specification of the random part
		10.4.1 Testing for heteroscedasticity
		10.4.2 What to do in case of heteroscedasticity
	10.5 Inspection of level-one residuals
	10.6 Residuals at level two
	10.7 Influence of level-two units
	10.8 More general distributional assumptions
	10.9 Glommary
11 Designing Multilevel Studies
	11.1 Some introductory notes on power
	11.2 Estimating a population mean
	11.3 Measurement of subjects
	11.4 Estimating association between variables
		11.4.1 Cross-level interaction effects
	11.5 Allocating treatment to groups or individuals
	11.6 Exploring the variance structure
		11.6.1 The intraclass correlation
		11.6.2 Variance parameters
	11.7 Glommary
12 Other Methods and Models
	12.1 Bayesian inference
	12.2 Sandwich estimators for standard errors
	12.3 Latent class models
	12.4 Glommary
13 Imperfect Hierarchies
	13.1 A two-level model with a crossed random factor
	13.2 Crossed random effects in three-level models
	13.3 Multiple membership models
	13.4 Multiple membership multiple classification models
	13.5 Glommary
14 Survey Weights
	14.1 Model-based and design-based inference
		14.1.1 Descriptive and analytic use of surveys
	14.2 Two kinds of weights
	14.3 Choosing between model-based and design-based analysis
		14.3.1 Inclusion probabilities and two-level weights
		14.3.2 Exploring the informativeness of the sampling design
	14.4 Example: Metacognitive strategies as measured in the PISA study
		14.4.1 Sampling design
		14.4.2 Model-based analysis of data divided into parts
		14.4.3 Inclusion of weights in the model
	14.5 How to assign weights in multilevel models
	14.6 Appendix. Matrix expressions for the single-level estimators
	14.7 Glommary
15 Longitudinal Data
	15.1 Fixed occasions
		15.1.1 The compound symmetry model
		15.1.2 Random slopes
		15.1.3 The fully multivariate model
		15.1.4 Multivariate regression analysis
		15.1.5 Explained variance
	15.2 Variable occasion designs
		15.2.1 Populations of curves
		15.2.2 Random functions
		15.2.3 Explaining the functions
		15.2.4 Changing covariates
	15.3 Autocorrelated residuals
	15.4 Glommary
16 Multivariate Multilevel Models
	16.1 Why analyze multiple dependent variables simultaneously?
	16.2 The multivariate random intercept model
	16.3 Multivariate random slope models
	16.4 Glommary
17 Discrete Dependent Variables
	17.1 Hierarchical generalized linear models
	17.2 Introduction to multilevel logistic regression
		17.2.1 Heterogeneous proportions
		17.2.2 The logit function: Log-odds
		17.2.3 The empty model
		17.2.4 The random intercept model
		17.2.5 Estimation
		17.2.6 Aggregation
	17.3 Further topics on multilevel logistic regression
		17.3.1 Random slope model
		17.3.2 Representation as a threshold model
		17.3.3 Residual intraclass correlation coefficient
		17.3.4 Explained variance
		17.3.5 Consequences of adding effects to the model
	17.4 Ordered categorical variables
	17.5 Multilevel event history analysis
	17.6 Multilevel Poisson regression
	17.7 Glommary
18 Software
	18.1 Special software for multilevel modeling
		18.1.1 HLM
		18.1.2 MLwiN
		18.1.3 The MIXOR suite and SuperMix
	18.2 Modules in general-purpose software packages
		18.2.1 SAS procedures VARCOMP, MIXED, GLIMMIX, and NLMIXED
		18.2.2 R
		18.2.3 Stata
		18.2.4 SPSS, commands VARCOMP and MIXED
	18.3 Other multilevel software
		18.3.1 PinT
		18.3.2 Optimal Design
		18.3.3 MLPowSim
		18.3.4 Mplus
		18.3.5 Latent Gold
		18.3.6 REALCOM
		18.3.7 WinBUGS
References
Index