Handbook of Multilevel Analysis

Foreword

Contents

List of Contributors

1 Introduction to Multilevel Analysis

1.1 History

1.2 Application Areas

1.3 Chapter Outline

1.4 Models

1.5 Loss Functions

1.6 Techniques and Algorithms

1.7 Software

1.8 Sampling Weights

1.9 A School Effects Example

1.10 Final Remarks

Appendix

References

2 Bayesian Multilevel Analysis and MCMC

2.1 Introduction

2.2 The Need for Simulation-Based Bayesian Computation

2.3 Markov Chain Monte Carlo (MCMC) Methods

2.4 MCMC Diagnostics

2.5 The Case Study Revisited

References

3 Diagnostic Checks for Multilevel Models

3.1 Specification of the Two-Level Model

3.2 Model Checks Within the Framework of the Hierarchical Linear Model

3.3 Residuals

3.4 Influence Diagnostics of Higher-Level Units

3.5 Simulation-Based Assessment of Model Specification

3.6 Non-linear Transformations in the Fixed Part

3.7 Polynomial Model

3.8 Regression Spline Model

3.9 Smoothing Spline Model

3.10 Example: Effect of IQ on a Language Test

3.11 Extensions

References

4 Optimal Designs for Multilevel Studies

4.1 Introduction

4.2 Optimality and Power

4.3 Optimal Designs for Experiments

4.4 Optimal Experimental Designs for Models with Covariates

4.5 Optimal Experimental Designs for Multilevel Logistic Models

4.6 Optimal Experimental Designs for Longitudinal Data

4.7 Optimal Designs for Surveys

4.8 Optimal Designs for Variance Parameters

4.9 Robustness of Optimal Designs

4.10 Concluding Remarks

References

5 Many Small Groups

5.1 Introduction

5.2 The Model

5.3 Some Applications

5.4 Validity of Statistical Inferences: Linear-Normal Case

5.5 Validity of Statistical Inferences: Non-Linear Link Functions

References

6 Multilevel Models for Ordinal and Nominal Variables

6.1 Introduction

6.2 Multilevel Logistic Regression Model

6.3 Multilevel Proportional Odds Model

6.4 Multilevel Nominal Response Models

6.5 Computational Issues

6.6 Intraclass Correlation

6.7 Heterogeneous Variance Terms

6.8 Health Services Research Example

6.9 Discussion

References

7 Multilevel and Related Models for Longitudinal Data

7.1 Introduction

7.2 Models with Unit-Specific Intercepts

7.3 Models with Unit-Specific Intercepts and Slopes

7.4 Models with Correlated Residual Errors

7.5 Models with Lagged Responses

7.6 Marginal Approaches

7.7 Concluding Remarks

References

8 Non-Hierarchical Multilevel Models

8.1 Introduction

8.2 Cross-Classified Models

8.3 Multiple Membership Models

8.4 Combining Multiple Membership and Cross- Classified Structures in a Single Model

8.5 Consequences of Ignoring Non-Hierarchical Structures

References

9 Multilevel Generalized Linear Models

9.1 Introduction

9.2 Extending Multilevel Models

9.3 Approaches to Estimation

9.4 Infant and Child Mortality in Kenya

9.5 Summary and Conclusions

References

10 Missing Data

10.1 Background and Generalities

10.2 Models for Missing Values

10.3 EM Algorithm and Multiple Imputation

10.4 Multiple Imputation

10.5 Missing Values in Multilevel Data

10.6 Other Applications of EM and MI

10.7 Summary

References

11 Resampling Multilevel Models

11.1 Introduction

11.2 Model, ML Estimation, and Assumptions

11.3 General Theory of Bootstrap and Jackknife

11.4 Bootstrapping Two-Level Models

11.5 Jackknifing Two-Level Models

11.6 Software

11.7 Empirical Evidence

11.8 Extensions

References

12 Multilevel Structural Equation Modeling

12.1 Introduction

12.2 A General Two-Level Structural Equation Model

12.3 Maximum Likelihood for General Means and Covariance Structures

12.4 Fit Statistics and Hypothesis Testing

12.5 A Simple Illustration

12.6 Practical Applications

12.7 Conclusion and Discussion

Appendix

References

Author Index

Subject Index