Handbook of Multilevel Analysis (eBook)

Foreword 5
Contents 9
List of Contributors 11
1 Introduction to Multilevel Analysis 14
1.1 History 14
1.2 Application Areas 16
1.3 Chapter Outline 18
1.4 Models 19
1.5 Loss Functions 32
1.6 Techniques and Algorithms 37
1.7 Software 60
1.8 Sampling Weights 61
1.9 A School Effects Example 67
1.10 Final Remarks 72
Appendix 73
References 81
2 Bayesian Multilevel Analysis and MCMC 89
2.1 Introduction 89
2.2 The Need for Simulation-Based Bayesian Computation 103
2.3 Markov Chain Monte Carlo (MCMC) Methods 106
2.4 MCMC Diagnostics 133
2.5 The Case Study Revisited 139
References 147
3 Diagnostic Checks for Multilevel Models 152
3.1 Specification of the Two-Level Model 152
3.2 Model Checks Within the Framework of the Hierarchical Linear Model 153
3.3 Residuals 160
3.4 Influence Diagnostics of Higher-Level Units 170
3.5 Simulation-Based Assessment of Model Specification 171
3.6 Non-linear Transformations in the Fixed Part 172
3.7 Polynomial Model 173
3.8 Regression Spline Model 173
3.9 Smoothing Spline Model 175
3.10 Example: Effect of IQ on a Language Test 180
3.11 Extensions 182
References 183
4 Optimal Designs for Multilevel Studies 187
4.1 Introduction 187
4.2 Optimality and Power 189
4.3 Optimal Designs for Experiments 191
4.4 Optimal Experimental Designs for Models with Covariates 196
4.5 Optimal Experimental Designs for Multilevel Logistic Models 198
4.6 Optimal Experimental Designs for Longitudinal Data 200
4.7 Optimal Designs for Surveys 203
4.8 Optimal Designs for Variance Parameters 207
4.9 Robustness of Optimal Designs 208
4.10 Concluding Remarks 210
References 211
5 Many Small Groups 216
5.1 Introduction 216
5.2 The Model 219
5.3 Some Applications 224
5.4 Validity of Statistical Inferences: Linear-Normal Case 233
5.5 Validity of Statistical Inferences: Non-Linear Link Functions 239
References 243
6 Multilevel Models for Ordinal and Nominal Variables 246
6.1 Introduction 246
6.2 Multilevel Logistic Regression Model 247
6.3 Multilevel Proportional Odds Model 252
6.4 Multilevel Nominal Response Models 259
6.5 Computational Issues 262
6.6 Intraclass Correlation 264
6.7 Heterogeneous Variance Terms 265
6.8 Health Services Research Example 267
6.9 Discussion 275
References 277
7 Multilevel and Related Models for Longitudinal Data 284
7.1 Introduction 284
7.2 Models with Unit-Specific Intercepts 286
7.3 Models with Unit-Specific Intercepts and Slopes 292
7.4 Models with Correlated Residual Errors 297
7.5 Models with Lagged Responses 299
7.6 Marginal Approaches 301
7.7 Concluding Remarks 304
References 304
8 Non-Hierarchical Multilevel Models 309
8.1 Introduction 309
8.2 Cross-Classified Models 309
8.3 Multiple Membership Models 328
8.4 Combining Multiple Membership and Cross- Classified Structures in a Single Model 335
8.5 Consequences of Ignoring Non-Hierarchical Structures 340
References 341
9 Multilevel Generalized Linear Models 343
9.1 Introduction 343
9.2 Extending Multilevel Models 345
9.3 Approaches to Estimation 354
9.4 Infant and Child Mortality in Kenya 366
9.5 Summary and Conclusions 378
References 379
10 Missing Data 385
10.1 Background and Generalities 385
10.2 Models for Missing Values 389
10.3 EM Algorithm and Multiple Imputation 391
10.4 Multiple Imputation 393
10.5 Missing Values in Multilevel Data 395
10.6 Other Applications of EM and MI 402
10.7 Summary 405
References 406
11 Resampling Multilevel Models 408
11.1 Introduction 408
11.2 Model, ML Estimation, and Assumptions 410
11.3 General Theory of Bootstrap and Jackknife 412
11.4 Bootstrapping Two-Level Models 417
11.5 Jackknifing Two-Level Models 427
11.6 Software 430
11.7 Empirical Evidence 431
11.8 Extensions 434
References 436
12 Multilevel Structural Equation Modeling 441
12.1 Introduction 441
12.2 A General Two-Level Structural Equation Model 442
12.3 Maximum Likelihood for General Means and Covariance Structures 445
12.4 Fit Statistics and Hypothesis Testing 450
12.5 A Simple Illustration 451
12.6 Practical Applications 454
12.7 Conclusion and Discussion 461
Appendix 464
References 482
Author Index 485
Subject Index 490