H. Goldstein

Multilevel Statistical Models (eBook, PDF)

• Format: PDF

Produktbeschreibung

Throughout the social, medical and other sciences the importance of understanding complex hierarchical data structures is well understood. Multilevel modelling is now the accepted statistical technique for handling such data and is widely available in computer software packages. A thorough understanding of these techniques is therefore important for all those working in these areas. This new edition of Multilevel Statistical Models brings these techniques together, starting from basic ideas and illustrating how more complex models are derived. Bayesian methodology using MCMC has been extended along with new material on smoothing models, multivariate responses, missing data, latent normal transformations for discrete responses, structural equation modeling and survival models. Key Features: * Provides a clear introduction and a comprehensive account of multilevel models. * New methodological developments and applications are explored. * Written by a leading expert in the field of multilevel methodology. * Illustrated throughout with real-life examples, explaining theoretical concepts. This book is suitable as a comprehensive text for postgraduate courses, as well as a general reference guide. Applied statisticians in the social sciences, economics, biological and medical disciplines will find this book beneficial.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 384
• Erscheinungstermin: 15. August 2010
• Englisch
• ISBN-13: 9780470973400
• Artikelnr.: 37301219

Autorenporträt

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.

Inhaltsangabe

Contents Dedication Preface Acknowledgements Notation A general
classification notation and diagram Glossary Chapter 1 An introduction to
multilevel models 1.1 Hierarchically structured data 1.2 School
effectiveness 1.3 Sample survey methods 1.4 Repeated measures data 1.5
Event history and survival models 1.6 Discrete response data 1.7
Multivariate models 1.8 Nonlinear models 1.9 Measurement errors 1.10 Cross
classifications and multiple membership structures. 1.11 Factor analysis
and structural equation models 1.12 Levels of aggregation and ecological
fallacies 1.13 Causality 1.14 The latent normal transformation and missing
data 1.15 Other texts 1.16 A caveat Chapter 2 The 2-level model 2.1
Introduction 2.2 The 2-level model 2.3 Parameter estimation 2.4 Maximum
likelihood estimation using Iterative Generalised Least Squares (IGLS) 2.5
Marginal models and Generalized Estimating Equations (GEE) 2.6 Residuals
2.7 The adequacy of Ordinary Least Squares estimates. 2.8 A 2-level example
using longitudinal educational achievement data 2.9 General model
diagnostics 2.10 Higher level explanatory variables and compositional
effects 2.11 Transforming to normality 2.12 Hypothesis testing and
confidence intervals 2.13 Bayesian estimation using Markov Chain Monte
Carlo (MCMC) 2.14 Data augmentation Appendix 2.1 The general structure and
maximum likelihood estimation for a multilevel model Appendix 2.2
Multilevel residuals estimation Appendix 2.3 Estimation using profile and
extended likelihood Appendix 2.4 The EM algorithm Appendix 2.5 MCMC
sampling Chapter 3. Three level models and more complex hierarchical
structures. 3.1 Complex variance structures 3.2 A 3-level complex variation
model example. 3.3 Parameter Constraints 3.4 Weighting units 3.5 Robust
(Sandwich) Estimators and Jacknifing 3.6 The bootstrap 3.7 Aggregate level
analyses 3.8 Meta analysis 3.9 Design issues Chapter 4. Multilevel Models
for discrete response data 4.1 Generalised linear models 4.2 Proportions as
responses 4.3 Examples 4.4 Models for multiple response categories 4.5
Models for counts 4.6 Mixed discrete - continuous response models 4.7 A
latent normal model for binary responses 4.8 Partitioning variation in
discrete response models Appendix 4.1. Generalised linear model estimation
Appendix 4.2 Maximum likelihood estimation for generalised linear models
Appendix 4.3 MCMC estimation for generalised linear models Appendix 4.4.
Bootstrap estimation for generalised linear models Chapter 5. Models for
repeated measures data 5.1 Repeated measures data 5.2 A 2-level repeated
measures model 5.3 A polynomial model example for adolescent growth and the
prediction of adult height 5.4 Modelling an autocorrelation structure at
level 1. 5.5 A growth model with autocorrelated residuals 5.6 Multivariate
repeated measures models 5.7 Scaling across time 5.8 Cross-over designs 5.9
Missing data 5.10 Longitudinal discrete response data Chapter 6.
Multivariate multilevel data 6.1 Introduction 6.2 The basic 2-level
multivariate model 6.3 Rotation Designs 6.4 A rotation design example using
Science test scores 6.5 Informative response selection: subject choice in
examinations 6.6 Multivariate structures at higher levels and future
predictions 6.7 Multivariate responses at several levels 6.8 Principal
Components analysis Appendix 6.1 MCMC algorithm for a multivariate normal
response model with constraints Chapter 7. Latent normal models for
multivariate data 7.1 The normal multilevel multivariate model 7.2 Sampling
binary responses 7.3 Sampling ordered categorical responses 7.4 Sampling
unordered categorical responses 7.5 Sampling count data 7.6 Sampling
continuous non-normal data 7.7 Sampling the level 1 and level 2 covariance
matrices 7.8 Model fit 7.9 Partially ordered data 7.10 Hybrid
normal/ordered variables 7.11 Discussion Chapter 9. Nonlinear multilevel
models 9.1 Introduction 9.2 Nonlinear functions of linear components 9.3
Estimating population means 9.4 Nonlinear functions for variances and
covariances 9.5 Examples of nonlinear growth and nonlinear level 1 variance
Appendix 9.1 Nonlinear model estimation Chapter 10. Multilevel modelling in
sample surveys 10.1 Sample survey structures 10.2 Population structures
10.3 Small area estimation Chapter 11 Multilevel event history and survival
models 11.1 Introduction 11.2 Censoring 11.3 Hazard and survival funtions
11.4 Parametric proportional hazard models 11.5 The semiparametric Cox
model 11.6 Tied observations 11.7 Repeated events proportional hazard
models 11.8 Example using birth interval data 11.9 Log duration models
11.10 Examples with birth interval data and children's activity episodes
11.11 The grouped discrete time hazards model 11.12 Discrete time latent
normal event history models Chapter 12. Cross classified data structures
12.1 Random cross classifications 12.2 A basic cross classified model 12.3
Examination results for a cross classification of schools 12.4 Interactions
in cross classifications 12.5 Cross classifications with one unit per cell
12.6 Multivariate cross classified models 12.7 A general notation for cross
classifications 12.8 MCMC estimation in cross classified models Appendix
12.1 IGLS Estimation for cross classified data. Chapter 13 Multiple
membership models 13.1 Multiple membership structures 13.2 Notation and
classifications for multiple membership structures 13.3 An example of
salmonella infection 13.4 A repeated measures multiple membership model
13.5 Individuals as higher level units 13.5.1 Example of research grant
awards 13.6 Spatial models 13.7 Missing identification models Appendix 13.1
MCMC estimation for multiple membership models. Chapter 14 Measurement
errors in multilevel models 14.1 A basic measurement error model 14.2
Moment based estimators 14.3 A 2-level example with measurement error at
both levels. 14.4 Multivariate responses 14.5 Nonlinear models 14.6
Measurement errors for discrete explanatory variables 14.7 MCMC estimation
for measurement error models Appendix 14.1 Measurement error estimation
14.2 MCMC estimation for measurement error models Chapter 15. Smoothing
models for multilevel data. 15.1 Introduction 15.2. Smoothing estimators
15.3 Smoothing splines 15.4 Semi parametric smoothing models 15.5
Multilevel smoothing models 15.6 General multilevel semi-parametric
smoothing models 15.7 Generalised linear models 15.8 An example Fixed
Random 15.9 Conclusions Chapter 16. Missing data, partially observed data
and multiple imputation 16.1 Creating a completed data set 16.2 Joint
modelling for missing data 16.3 A two level model with responses of
different types at both levels. 16.4 Multiple imputation 16.5 A simulation
example of multiple imputation for missing data 16.6 Longitudinal data with
attrition 16.7 Partially known data values 16.8 Conclusions Chapter 17
Multilevel models with correlated random effects 17.1 Non-independence of
level 2 residuals 17.2 MCMC estimation for non-independent level 2
residuals 17.3 Adaptive proposal distributions in MCMC estimation 17.4 MCMC
estimation for non-independent level 1 residuals 17.5 Modelling the level 1
variance as a function of explanatory variables with random effects 17.6
Discrete responses with correlated random effects 17.7 Calculating the DIC
statistic 17.8 A growth data set 17.9 Conclusions Chapter 18. Software for
multilevel modelling References Author index Subject index