CONTENTS
Preface = ⅸ
Acknowledgements = ⅹ
Notation = xi
Glossary = xiii
1 Introduction = 1
Introduction = 1
School effectiveness = 3
Sample survey methods = 5
Repeated measures data = 5
Event history models = 6
Discrete response data = 7
Multivariate models = 7
Nonlinear models = 8
Measurement errors = 8
Random cross classifications = 9
Structural equation models = 10
Levels of aggregation and ecological fallacies = 10
Causality = 11
A caveat = 12
2 The Basic Linear Multilevel Model and its Estimation = 15
The 2-level model and basic notation = 15
The 2-level model = 17
Parameter estimation for the variance components model = 18
The general 2-level model including random coefficients = 20
Estimation for the multilevel model = 21
Other estimation procedures = 23
Residuals = 24
The adequacy of Ordinary Least Squares estimates = 25
A 2-level example using longitudinal educational achievement data = 26
Higher level explanatory variables and compositional effects = 30
Hypothesis testing and confidence intervals = 32
Appendix 2.1 The general structure and estimation for a multilevel model = 38
Appendix 2.2 Multilevel residuals estimation = 41
Appendix 2.3 The EM algorithm = 43
Appendix 2.4 Gibbs sampling = 45
3 Extensions to the Basic Multilevel Model = 47
Complex variance structures = 47
A 3-level complex variation model = 55
Parameter constraints = 57
Weighting units = 58
Robust, jackknife and bootstrap uncertainty estimates = 60
Aggregate level analyses = 62
Meta analysis = 65
4 The Multivariate Multilevel Model = 69
Multivariate multilevel models = 69
The basic 2-level multivariate model = 69
Rotation designs = 71
A rotation design example using science test scores = 72
Principal components analysis = 74
Multiple discriminant analysis = 76
Other procedures = 76
5 Nonlinear Multilevel Models = 77
Nonlinear models = 77
Nonlinear functions of linear components = 77
Estimating population means = 79
Nonlinear functions for variances and covariances = 80
Examples of nonlinear growth and nonlinear level 1 variance = 80
Multivariate nonlinear models = 82
Appendix 5.1 Nonlinear model estimation = 83
6 Models for Repeated Measures Data = 87
Models for repeated measures = 87
A 2-level repeated measures model = 88
A polynomial model example for adolescent growth and the prediction of adult height = 88
Modelling an autocorrelation structure at level 1 = 91
A growth model with autocorrelated residuals = 92
Multivariate repeated measures models = 94
Scaling across time = 94
Cross-over designs = 94
7 Multilevel Models for Discrete Response Data = 97
Models for discrete response data = 97
Proportions as responses = 98
An example from a survey of voting behaviour = 101
Models for multiple response categories = 104
An example of voting behaviour with multiple responses = 106
Models for counts = 106
Ordered responses = 108
Mixed discrete-continuous response models = 109
Appendix 7.1 Differentials for some discrete response models = 112
8 Multilevel Cross Classification = 113
Random cross classifications = 113
A basic cross classified model = 116
Examination results for a cross classification of schools = 117
Computational considerations = 118
Interactions in cross classifications = 119
Level 1 cross classifications = 120
Cross-unit membership models = 120
Multivariate cross classified models = 121
Appendix 8.1 Random cross classified data structures = 123
9 Multilevel Event History Models = 125
Event history models = 125
Censoring = 125
Hazard-based models in continuous time = 126
Parametric proportional hazard models = 127
The semiparametric Cox model = 127
Tied observations = 129
Repeated measures proportional hazard models = 129
Example using birth interval data = 130
The discrete time (piecewise) proportional hazards model = 132
Log duration models = 132
Censored data = 134
Infinite durations = 136
Examples with birth interval data and children's play episodes = 136
10 Multilevel Models with Measurement Errors = 141
Errors of measurement = 141
Measurement errors in level 1 variables = 142
Measurement errors in higher level variables = 143
A 2-level example with measurement error at both levels = 145
Multivariate responses = 147
Nonlinear models = 147
Measurement errors for discrete explanatory variables = 147
Appendix 10.1 Measurement errors = 149
11 Software for Multilevel Modelling; Missing Data and Multilevel Structural Equation Models = 153
Software for multilevel analysis = 153
Design issues = 154
Missing data = 155
Creating a completed data set = 155
Multiple imputation and error corrections = 156
Discrete variables with missing data = 158
An example with missing data = 158
Multilevel structural equation models = 159
A factor analysis example using science test scores = 161
Future developments = 161
Appendix 11.1 Addresses for multilevel software packages = 163
References = 165
Author Index = 171
Subject Index = 173
