Generalized Latent Variable Modeling : Multilevel, Longitudinal, and Structural Equation Models book cover
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Generalized Latent Variable Modeling
Multilevel, Longitudinal, and Structural Equation Models




ISBN 9781584880004
Published May 11, 2004 by Chapman and Hall/CRC
528 Pages 62 B/W Illustrations

 
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Book Description

This book unifies and extends latent variable models, including multilevel or generalized linear mixed models, longitudinal or panel models, item response or factor models, latent class or finite mixture models, and structural equation models. Following a gentle introduction to latent variable modeling, the authors clearly explain and contrast a wide range of estimation and prediction methods from biostatistics, psychometrics, econometrics, and statistics. They present exciting and realistic applications that demonstrate how researchers can use latent variable modeling to solve concrete problems in areas as diverse as medicine, economics, and psychology. The examples considered include many nonstandard response types, such as ordinal, nominal, count, and survival data. Joint modeling of mixed responses, such as survival and longitudinal data, is also illustrated. Numerous displays, figures, and graphs make the text vivid and easy to read.

About the authors:

Anders Skrondal is Professor and Chair in Social Statistics, Department of Statistics, London School of Economics, UK

Sophia Rabe-Hesketh is a Professor of Educational Statistics at the Graduate School of Education and Graduate Group in Biostatistics, University of California, Berkeley, USA.

Table of Contents

METHODOLOGY
THE OMNI-PRESENCE OF LATENT VARIABLES
Introduction
‘True’ variable measured with error
Hypothetical constructs
Unobserved heterogeneity
Missing values and counterfactuals
Latent responses
Generating flexible distributions
Combining information
Summary
MODELING DIFFERENT RESPONSE PROCESSES
Introduction
Generalized linear models
Extensions of generalized linear models
Latent response formulation
Modeling durations or survival
Summary and further reading
CLASSICAL LATENT VARIABLE MODELS
Introduction
Multilevel regression models
Factor models and item response models
Latent class models
Structural equation models with latent variables
Longitudinal models
Summary and further reading
GENERAL MODEL FRAMEWORK
Introduction
Response model
Structural model for the latent variables
Distribution of the disturbances
Parameter restrictions and fundamental parameters
Reduced form of the latent variables and linear predictor
Moment structure of the latent variables
Marginal moment structure of observed and latent responses
Reduced form distribution and likelihood
Reduced form parameters
Summary and further reading
IDENTIFICATION AND EQUIVALENCE
Introduction
Identification
Equivalence
Summary and further reading
ESTIMATION
Introduction
Maximum likelihood: Closed form marginal likelihood
Maximum likelihood: Approximate marginal likelihood
Maximizing the likelihood
Nonparametric maximum likelihood estimation
Restricted/Residual maximum likelihood (REML)
Limited information methods
Maximum quasi-likelihood
Generalized Estimating Equations (GEE)
Fixed effects methods
Bayesian methods
Summary
Appendix: Some software and references
ASSIGNING VALUES TO LATENT VARIABLES
Introduction
Posterior distributions
Empirical Bayes (EB)
Empirical Bayes modal (EBM)
Maximum likelihood
Relating the scoring methods in the ‘linear case’
Ad hoc scoring methods
Some uses of latent scoring and classification
Summary and further reading
Appendix: Some software
MODEL SPECIFICATION AND INFERENCE
Introduction
Statistical modeling
Inference (likelihood based)
Model selection: Relative fit criteria
Model adequacy: Global absolute fit criteria
Model diagnostics: Local absolute fit criteria
Summary and further reading
APPLICATIONS
DICHOTOMOUS RESPONSES
Introduction
Respiratory infection in children: A random intercept model
Diagnosis of myocardial infarction: A latent class model
Arithmetic reasoning: Item response models
Nicotine gum and smoking cessation: A meta-analysis
Wives’ employment transitions: Markov models with unobserved heterogeneity
Counting snowshoe hares: Capture-recapture models with heterogeneity
Attitudes to abortion: A multilevel item response model
Summary and further reading
ORDINAL RESPONSES
Introduction
Cluster randomized trial of sex education: Latent growth curve model
Political efficacy: Factor dimensionality and item-bias
Life satisfaction: Ordinal scaled probit factor models
Summary and further reading
COUNTS
Introduction
Prevention of faulty teeth in children: Modeling overdispersion
Treatment of epilepsy: A random coefficient model
Lip cancer in Scotland: Disease mapping
Summary and further reading
DURATIONS AND SURVIVAL
Introduction
Modeling multiple events clustered duration data
Onset of smoking: Discrete time frailty models
Exercise and angina: Proportional hazards random effects and factor models
Summary and further reading
COMPARATIVE RESPONSES
Introduction
Heterogeneity and ‘Independence from Irrelevant Alternatives’
Model structure
British general elections: Multilevel models for discrete choice and rankings
Post-materialism: A latent class model for rankings
Consumer preferences for coffee makers: A conjoint choice model
Summary and further reading
MULTIPLE PROCESSES AND MIXED RESPONSES
Introduction
Diet and heart disease: A covariate measurement error model
Herpes and cervical cancer: A latent class covariate measurement error model for a case-control study
Job training and depression: A complier average causal effect model
Physician advice and drinking: An endogenous treatment model
Treatment of liver cirrhosis: A joint survival and marker model
Summary and further reading
REFERENCES
INDEX
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Author - Sophia  Rabe-Hesketh
Author

Sophia Rabe-Hesketh

Professor, University of California, Berkeley
Berkeley, CA, USA

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Reviews

“… an extremely useful resource for statisticians working in medical and biological sciences and social sciences such as economics and psychology. Most statisticians apply some form of latent variable modeling in their research, and this book presents the latest developments in the field in a clear and engaging way.”
— Fiona Steele, University of Bristol, in Statistical Methods in Medical Research,, 2008, Vol. 17

“… an elegant and illuminating unification of concepts and models from diverse disciplines. The final application chapters deal with a broad collection of interesting applications to areas, such as meta-analyses, disease mapping, confirmatory factor analysis, and case-control studies. The book is well worth acquiring and would be a suitable text for advanced graduate courses.”
ISI Short Book Reviews

“Written by well-known experts in biostatistics and educational statistics, it presents a uniform approach to enriching both theoretical and applied latent variables modeling that also can be used in any branch of natural science or technical and engineering application. … Numerous interesting examples … are considered. … Written in a very friendly and mathematically clear language, rigorous but not overloaded with redundant pure statistical derivations, the book could be exceptionally useful for practitioners. … This book is a really enjoyable and useful reading for graduate students and researchers along with [those] from any field who wish to use modern statistical techniques to solve practical problems.”
Technometrics, May 2005, Vol. 47, No. 2

“This is perhaps the only book that uses the ‘latent’ modeling framework to address a range of data analytical situations. … it provided a great introduction to this field.”
—Dr. S.V. Subramanian, Harvard University

“This is a very impressive book … an excellent book. I have no hesitation in recommending readers to buy this book.”
The Stata Journal, 2005

“Who will profit from reading this book? On the one hand, it is a book written for people who like to construct and read about very general theories and modeling strategies. It is also a very useful book for statisticians who have specialized in one area … and would like to learn more about another area. The book itself is very well-written. The presentation is concise; many issues are well illustrated graphically. [T]he authors have written an excellent, imaginative, and authoritative text on the difficult topic of modeling the problems of multivariate outcomes with different scaling levels, different units of analysis, and different study designs simultaneously.”
Biometrics, March 2005

“It has two fundamental features that make it one of the most comprehensive reference books in the field: an up-to-date guide to multilevel and structural latent variable modeling and estimation, plus a multidisciplinary set of illustrative examples … these are extremely enlightening for experienced practitioners in the many areas in which latent variable modeling can be used to analyze data … to my knowledge, the present book is the first to provide a truly unifying generalized approach to latent variable modeling … I find the book to be an exceedingly valuable reference that would be ideal for graduate-level courses on generalized latent variable modeling. It is very straightforward to build from it a comprehensive course where the statistical section is complemented with a multidisciplinary set of easily replicated examples, because both the data sets and the software are available online … the book’s impressive breadth and depth make it an essential reference for any researchers interested in understanding the state-of-the-art methods and potential applications in latent multilevel, longitudinal, and structural equation modeling.”
Journal of the American Statistical Association

“[This book] provides a useful summary and references… . [It] illustrates the close connection between models for discrete choice data common in econometrics and IRT.”
Psychometrika