| |
| |
| Dedication | |
| |
| |
| Preface | |
| |
| |
| Acknowledgements | |
| |
| |
| Notation | |
| |
| |
| A general classification notation and diagram | |
| |
| |
| Glossary | |
| |
| |
| |
| An introduction to multilevel models | |
| |
| |
| |
| Hierarchically structured data | |
| |
| |
| |
| School effectiveness | |
| |
| |
| |
| Sample survey methods | |
| |
| |
| |
| Repeated measures data | |
| |
| |
| |
| Event history and survival models | |
| |
| |
| |
| Discrete response data | |
| |
| |
| |
| Multivariate models | |
| |
| |
| |
| Nonlinear models | |
| |
| |
| |
| Measurement errors | |
| |
| |
| |
| Cross classifications and multiple membership structures | |
| |
| |
| |
| Factor analysis and structural equation models | |
| |
| |
| |
| Levels of aggregation and ecological fallacies | |
| |
| |
| |
| Causality | |
| |
| |
| |
| The latent normal transformation and missing data | |
| |
| |
| |
| Other texts | |
| |
| |
| |
| A caveat | |
| |
| |
| |
| The 2-level model | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| The 2-level model | |
| |
| |
| |
| Parameter estimation | |
| |
| |
| |
| Maximum likelihood estimation using Iterative Generalised Least Squares (IGLS) | |
| |
| |
| |
| Marginal models and Generalized Estimating Equations (GEE) | |
| |
| |
| |
| Residuals | |
| |
| |
| |
| The adequacy of Ordinary Least Squares estimates | |
| |
| |
| |
| A 2-level example using longitudinal educational achievement data | |
| |
| |
| |
| General model diagnostics | |
| |
| |
| |
| Higher level explanatory variables and compositional effects | |
| |
| |
| |
| Transforming to normality | |
| |
| |
| |
| Hypothesis testing and confidence intervals | |
| |
| |
| |
| Bayesian estimation using Markov Chain Monte Carlo (MCMC) | |
| |
| |
| |
| Data augmentation | |
| |
| |
| |
| The general structure and maximum likelihood estimation for a multilevel model | |
| |
| |
| |
| Multilevel residuals estimation | |
| |
| |
| |
| Estimation using profile and extended likelihood | |
| |
| |
| |
| The EM algorithm | |
| |
| |
| |
| MCMC sampling | |
| |
| |
| |
| Three level models and more complex hierarchical structures | |
| |
| |
| |
| Complex variance structures | |
| |
| |
| |
| A 3-level complex variation model example | |
| |
| |
| |
| Parameter Constraints | |
| |
| |
| |
| Weighting units | |
| |
| |
| |
| Robust (Sandwich) Estimators and Jacknifing | |
| |
| |
| |
| The bootstrap | |
| |
| |
| |
| Aggregate level analyses | |
| |
| |
| |
| Meta analysis | |
| |
| |
| |
| Design issues | |
| |
| |
| |
| Multilevel Models for discrete response data | |
| |
| |
| |
| Generalised linear models | |
| |
| |
| |
| Proportions as responses | |
| |
| |
| |
| Examples | |
| |
| |
| |
| Models for multiple response categories | |
| |
| |
| |
| Models for counts | |
| |
| |
| |
| Mixed discrete - continuous response models | |
| |
| |
| |
| A latent normal model for binary responses | |
| |
| |
| |
| Partitioning variation in discrete response models | |
| |
| |
| |
| Generalised linear model estimation | |
| |
| |
| |
| Maximum likelihood estimation for generalised linear models | |
| |
| |
| |
| MCMC estimation for generalised linear models | |
| |
| |
| |
| Bootstrap estimation for generalised linear models | |
| |
| |
| |
| Models for repeated measures data | |
| |
| |
| |
| Repeated measures data | |
| |
| |
| |
| A 2-level repeated measures model | |
| |
| |
| |
| A polynomial model example for adolescent growth and the prediction of adult height | |
| |
| |
| |
| Modelling an autocorrelation structure at level 1 | |
| |
| |
| |
| A growth model with autocorrelated residuals | |
| |
| |
| |
| Multivariate repeated measures models | |
| |
| |
| |
| Scaling across time | |
| |
| |
| |
| Cross-over designs | |
| |
| |
| |
| Missing data | |
| |
| |
| |
| Longitudinal discrete response data | |
| |
| |
| |
| Multivariate multilevel data | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| The basic 2-level multivariate model | |
| |
| |
| |
| Rotation Designs | |
| |
| |
| |
| A rotation design example using Science test scores | |
| |
| |
| |
| Informative response selection: subject choice in examinations | |
| |
| |
| |
| Multivariate structures at higher levels and future predictions | |
| |
| |
| |
| Multivariate responses at several levels | |
| |
| |
| |
| Principal Components analysis | |
| |
| |
| |
| MCMC algorithm for a multivariate normal response model with constraints | |
| |
| |
| |
| Latent normal models for multivariate data | |
| |
| |
| |
| The normal multilevel multivariate model | |
| |
| |
| |
| Sampling binary responses | |
| |
| |
| |
| Sampling ordered categorical responses | |
| |
| |
| |
| Sampling unordered categorical responses | |
| |
| |
| |
| Sampling count data | |
| |
| |
| |
| Sampling continuous non-normal data | |
| |
| |
| |
| Sampling the level 1 and level 2 covariance matrices | |
| |
| |
| |
| Model fit | |
| |
| |
| |
| Partially ordered data | |
| |
| |
| |
| Hybrid normal/ordered variables | |
| |
| |
| |
| Discussion | |
| |
| |
| |
| Nonlinear multilevel models | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Nonlinear functions of linear components | |
| |
| |
| |
| Estimating population means | |
| |
| |
| |
| Nonlinear functions for variances and covariances | |
| |
| |
| |
| Examples of nonlinear growth and nonlinear level 1 variance | |
| |
| |
| |
| Nonlinear model estimation | |
| |
| |
| |
| Multilevel modelling in sample surveys | |
| |
| |
| |
| Sample survey structures | |
| |
| |
| |
| Population structures | |
| |
| |
| |
| Small area estimation | |
| |
| |
| |
| Multilevel event history and survival models | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Censoring | |
| |
| |
| |
| Hazard and survival funtions | |
| |
| |
| |
| Parametric proportional hazard models | |
| |
| |
| |
| The semiparametric Cox model | |
| |
| |
| |
| Tied observations | |
| |
| |
| |
| Repeated events proportional hazard models | |
| |
| |
| |
| Example using birth interval data | |
| |
| |
| |
| Log duration models | |
| |
| |
| |
| Examples with birth interval data and children's activity episodes | |
| |
| |
| |
| The grouped discrete time hazards model | |
| |
| |
| |
| Discrete time latent normal event history models | |
| |
| |
| |
| Cross classified data structures | |
| |
| |
| |
| Random cross classifications | |
| |
| |
| |
| A basic cross classified model | |
| |
| |
| |
| Examination results for a cross classification of schools | |
| |
| |
| |
| Interactions in cross classifications | |
| |
| |
| |
| Cross classifications with one unit per cell | |
| |
| |
| |
| Multivariate cross classified models | |
| |
| |
| |
| A general notation for cross classifications | |
| |
| |
| |
| MCMC estimation in cross classified models | |
| |
| |
| Appendix 12.1 IGLS Estimation for cross classified data | |
| |
| |
| |
| Multiple membership models | |
| |
| |
| |
| Multiple membership structures | |
| |
| |
| |
| Notation and classifications for multiple membership structures | |
| |
| |
| |
| An example of salmonella infection | |
| |
| |
| |
| A repeated measures multiple membership model | |
| |
| |
| |
| Individuals as higher level units | |
| |
| |
| |
| Example of research grant awards | |
| |
| |
| |
| Spatial models | |
| |
| |
| |
| Missing identification models | |
| |
| |
| |
| MCMC estimation for multiple membership models | |
| |
| |
| |
| Measurement errors in multilevel models | |
| |
| |
| |
| A basic measurement error model | |
| |
| |
| |
| Moment based estimators | |
| |
| |
| |
| A 2-level example with measurement error at both levels | |
| |
| |
| |
| Multivariate responses | |
| |
| |
| |
| Nonlinear models | |
| |
| |
| |
| Measurement errors for discrete explanatory variables | |
| |
| |
| |
| MCMC estimation for measurement error models | |
| |
| |
| |
| Measurement error estimation | |
| |
| |
| |
| MCMC estimation for measurement error models | |
| |
| |
| |
| Smoothing models for multilevel data | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Smoothing estimators | |
| |
| |
| |
| Smoothing splines | |
| |
| |
| |
| Semi parametric smoothing models | |
| |
| |
| |
| Multilevel smoothing models | |
| |
| |
| |
| General multilevel semi-parametric smoothing models | |
| |
| |
| |
| Generalised linear models | |
| |
| |
| |
| An example | |
| |
| |
| Fixed | |
| |
| |
| Random | |
| |
| |
| |
| Conclusions | |
| |
| |
| |
| Missing data, partially observed data and multiple imputation | |
| |
| |
| |
| Creating a completed data set | |
| |
| |
| |
| Joint modelling for missing data | |
| |
| |
| |
| A two level model with responses of different types at both levels | |
| |
| |
| |
| Multiple imputation | |
| |
| |
| |
| A simulation example of multiple imputation for missing data | |
| |
| |
| |
| Longitudinal data with attrition | |
| |
| |
| |
| Partially known data values | |
| |
| |
| |
| Conclusions | |
| |
| |
| |
| Multilevel models with correlated random effects | |
| |
| |
| |
| Non-independence of level 2 residuals | |
| |
| |
| |
| MCMC estimation for non-independent level 2 residuals | |
| |
| |
| |
| Adaptive proposal distributions in MCMC estimation | |
| |
| |
| |
| MCMC estimation for non-independent level 1 residuals | |
| |
| |
| |
| Modelling the level 1 variance as a function of explanatory variables with random effects | |
| |
| |
| |
| Discrete responses with correlated random effects | |
| |
| |
| |
| Calculating the DIC statistic | |
| |
| |
| |
| A growth data set | |
| |
| |
| |
| Conclusions | |
| |
| |
| |
| Software for multilevel modelling | |
| |
| |
| References | |
| |
| |
| Author Index | |
| |
| |
| Subject Index | |