1st Edition

Generalized Latent Variable Modeling Multilevel, Longitudinal, and Structural Equation Models

    522 Pages 62 B/W Illustrations
    by Chapman & Hall

    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.

    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

    Biography

    Anders Skrondal, Sophia Rabe-Hesketh

    “… 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