Generalized Latent Variable Modeling

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

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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.show more

Product details

  • Hardback | 528 pages
  • 162 x 234 x 34mm | 861.84g
  • Taylor & Francis Inc
  • CRC Press Inc
  • Bosa Roca, United States
  • English
  • 62 black & white illustrations, 74 black & white tables
  • 1584880007
  • 9781584880004
  • 977,479

Review quote

"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 a book written for people who like to construct and to 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 is very well written. The presentation is concise; many issues are well illustrated graphically. Altogether, the authors have written an excellent, imaginative, and authoritative text ." - Biometrics 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 "Overall I found the book an exceedingly valuable reference that would be ideal for graduate-level courses devoted to generalized latent variable modeling. It is very straight forward to build around it a comprehensive course where the statistical section is complemented with amultidisciplinary set of illustrative examples which can be easily replicated as both the datasets and the software are available on-line. In addition, the impressive book's breadth and depth make it an essential reference for any researcher 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 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 to 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. Altogether the 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 examplesthese are extremely enlightening for experienced practitioners in the many areas in which latent variable modeling can be used to analyze datato my knowledge, thepresent book is the first to provide a truly unifying generalized approach to latent variable modelingI 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 datasets and the software are available onlinethe 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 Associationshow more

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 AUTHOR INDEXshow more

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