Generalized latent variable modeling. Multilevel, longitudinal, and structural equation models. (English) Zbl 1097.62001

Interdisciplinary Statistics. Boca Raton, FL: Chapman & Hall/CRC (ISBN 1-58488-000-7/hbk; 978-0-203-48943-7/ebook). xi, 508 p. (2004).
A major aim of this book is to unify and extend latent variable modeling in the widest sense. The models covered include multilevel, longitudinal and structural equation models as well as relatives and friends such as generalized linear mixed models, random coefficient models, item response models, factor models, panel models, repeated measurement models, latent class models and frailty models. Numerous displays, figures, and graphs make the book vivid and easy to read.
The book consists of two parts: methodology and applications. In Chapter 1 the concept, uses and interpretations of latent variables are discussed. In Chapter 2, a wide range of response processes are introduced and most of the processes can more or less be expressed as generalized linear models, and many as latent response models. The classical latent variable models are surveyed in Chapter 3, and these models are unified and extended in Chapter 4 for all response types surveyed in Chapter 2.
Established and novel methods of model identification, estimation, latent variable prediction and model diagnostics are extensively covered in Chapters 5 to 8.
In applications in Chapters 9 to 14, the methodology developed in the first part is used to address problems from biology, medicine, psychology, education, sociology, political science, economics, marketing and other areas. All applications are based on real data, but the analysis is often simplified for didactic reasons. The STATA program GLLAMM is used for all applications.
This book is an excellent reference book on generalized latent variable modeling. It may also serve as a textbook for a graduate course in generalized latent variable modeling. It is noted that exercises are not provided in this book.


62-02 Research exposition (monographs, survey articles) pertaining to statistics
62J12 Generalized linear models (logistic models)
65C60 Computational problems in statistics (MSC2010)
62Pxx Applications of statistics


absolute fit criteria; absorbing event; accelerated failure time model; acceptance probability; scoring; adaptive quadrature; adaptive rejection sampling; adjacent category logit model; Akaike information criterion; algorithmic model; alternating imputation posterior algorithm; alternating logistic regression; Anscombe residual; antedependence; bidimensional factor model; item-bias; capture-recapture model; complier average causal effect model; conjoint choice model; covariate measurement error model; discrete time frailty model; disease mapping; endogenous treatment model; item response model; joint survival and marker model; latent class covariate measurement error model for case-control studies; latent class model; latent growth curve model; Markov transition model; meta analysis; overdispersion; multilevel model; ordinal scaled probit factor model; proportional hazards latent variable model; random coefficient model; random intercept model; attenuation; autoregressive residuals; Bayes factor; Berkson error; best linear unbiased estimator; Bayesian information criterion; binomial logit-normal model; canonical link; censored response; classification; duration analysis; comparative response; complementary log-log link; conditional independence; conditional maximum likelihood; logit model; cross-validation; deviance; deviance information criterion; diagnostics; dichotomous response; disturbance distribution; empirical equivalence; empirical identification; empirical model; empirical Bayes; equivalence; expectation-maximization algorithm; exponential family; factor dimensionality; factor model; factor structure; finite mixture; Fisher information; fixed effects model; fundamental parameter; Gateaux derivative; Gauss-Hermite quadrature; generalized estimating equation; linear mixed model; Geweke-Hajivassiliou-Keane simulator; importance sampling; Gibbs sampler; generalized linear model; goodness of fit; gradient methods; Gumbel distribution; higher-level residual; hyperparameter; hyperprior; hypothetical construct; identification problem; identity link; influence; intraclass correlation; iterative generalized least squares; iterative reweighted least squares; Kullback-Leibler information; lagged response model; Laplace approximation; latent response; latent covariate; latent scoring; latent score estimation; latent score prediction; latent variable; level-1 residual; limited information method; link function; local identification; longitudinal model; log link; logit link; marginal moment structure; marginal quasi-likelihood; Markov chain Monte Carlo; Metropolis algorithm; Metropolis-Hastings algorithm; multiple-indicator multiple-cause model; missing values; mixture regression model; model selection; Monte Carlo integration; model-based standard error; multinomial response; Newton-Raphson algorithm; nominal response model; noninformative prior; nonparametric maximum likelihood; ordinal factor model; ordinal logit model; ordinal probit model; ordinal response; outlier; bootstrap; Pearson residual; penalized quasi-likelihood; Poisson regression; polychotomous response; population averaged effect; profile log-likelihood; quasi-likelihood; recursive model; reduced form; regression dilution; regular point; relative fit criteria; reliability; restricted maximum likelihood; right censoring; left censoring; robust standard error; factor loading; shrinkage; spatial model; structural equation model; structural parameter; substantive model; survival analysis; unit-specific effect; heteroscedasticity; homoscedasticity; utility; weighted least squares; binomial model; heterogeneity
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