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Generalized Latent Variable Modeling

Multilevel, Longitudinal, and Structural Equation Models

By Anders Skrondal, Sophia Rabe-Hesketh

Chapman and Hall/CRC – 2004 – 528 pages

Series: Chapman & Hall/CRC Interdisciplinary Statistics

Purchasing Options:

  • Add to CartHardback: $119.95
    978-1-58488-000-4
    May 11th 2004

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.

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

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

AUTHOR INDEX

Name: Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equation Models (Hardback)Chapman and Hall/CRC 
Description: By Anders Skrondal, Sophia Rabe-Hesketh. 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...
Categories: Quantitative Methods, Regression Analysis and Multivariate Statistics, Statistics for the Biological Sciences, Statistical Theory & Methods