Multilevel Statistical Models

ISBN-10: 0470748656
ISBN-13: 9780470748657
Edition: 4th 2011
Authors: Harvey Goldstein
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Description: 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  More...

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Book details

Edition: 4th
Copyright year: 2011
Publisher: John Wiley & Sons, Limited
Publication date: 10/22/2010
Binding: Hardcover
Pages: 384
Size: 6.50" wide x 9.50" long x 1.00" tall
Weight: 1.496
Language: English

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.

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

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