Multilevel Statistical Models
, by Goldstein, Harvey
- ISBN: 9780470748657 | 0470748656
- Cover: Hardcover
- Copyright: 11/3/2010
This book provides a clear introduction to this important area of statistics. The author provides a wide of coverage of different kinds of multilevel models, and how to interpret different statistical methodologies and algorithms applied to such models. This 4th edition reflects the growth and interest in this area and is updated to include new chapters on multilevel models with mixed response types, smoothing and multilevel data, models with correlated random effects and modeling with variance.
Harvey Goldstein, Professor of social sciences, University of Bristol and Associate Editor for the Statistical Modelling Journal, and previous Editor of the Royal Statistical Society's Journal, Series A.
| 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 | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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