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

Anders Skrondal and Sophia Rabe-Hesketh
Publisher: Chapman & Hall/CRC
Copyright: 2004
ISBN-13: 978-1-58488-000-4
Pages: 508; hardcover
Price: $79.75
Supplements:Datasets and do-files

Comment from the Stata technical group

This text unifies the principles behind latent variable modeling, which includes multilevel, longitudinal, and structural equation models, as well as generalized mixed models, random coefficient models, item response models, factor models, panel models, repeated-measures models, latent-class models, and frailty models. Since latent-variable models are used by researchers from various disciplines with little or no cross-referencing from other disciplines, unifying these models allows readers to separate what the authors refer to as local jargon from the fundamental elements of these models. As such, this text allows readers to gain quick and easy access to models and estimation schemes that have long existed in other disciplines but perhaps are not widely used in their own.

The book consists of two main parts: methodology and applications. Chapters 1–4 provide background information and generalized development of latent variable models. Chapters 5–8 are concerned with techniques of estimation, prediction, and inference. Chapters 9–14 comprise the applications portion of the text, and here the unification from chapters 1–4 is applied to case studies from various fields, including biostatistics, political science, social science, and econometrics.

The models demonstrated in the applications section are fitted using the Stata program gllamm, written by the authors of this text and available from

Table of contents

I Methodology
1 The omni-presence of latent variables
1.1 Introduction
1.2 ‘True’ variable measured with error
1.3 Hypothetical constructs
1.4 Unobserved heterogeneity
1.5 Missing values and counterfactual
s 1.6 Latent responses
1.7 Generating flexible distributions
1.8 Combining information
1.9 Summary
2 Modeling different response processes
2.1 Introduction
2.2 Generalized linear models
2.3 Extensions of generalized linear models
2.4 Latent response formulation
2.5 Modeling durations or survival
2.6 Summary and further reading
3 Classical latent variable models
3.1 Introduction
3.2 Multilevel regression models
3.3 Factor models and item response models
3.4 Latent class models
3.5 Structural equation models with latent variables
3.6 Longitudinal models
3.7 Summary and further reading
4 General model framework
4.1 Introduction
4.2 Response model
4.3 Structural model for the latent variables
4.4 Distribution of the disturbances
4.5 Parameter restrictions and fundamental parameters
4.6 Reduced form of the latent variables and linear predictor
4.7 Moment structure of the latent variables
4.8 Marginal moment structure of observed and latent response
s 4.9 Reduced form distribution and likelihood
4.10 Reduced form parameters
4.11 Summary and further reading
5 Identification and equivalence
5.1 Introduction
5.2 Identification
5.3 Equivalence
5.4 Summary and further reading
6 Estimation
6.1 Introduction
6.2 Maximum likelihood: Closed form marginal likelihood
6.3 Maximum likelihood: Approximate marginal likelihood
6.4 Maximizing the likelihood
6.5 Nonparametric maximum likelihood estimation
6.6 Restricted/Residual maximum likelihood (REML)
6.7 Limited information methods
6.8 Maximum quasi-likelihood
6.9 Generalized Estimating Equations (GEE
) 6.10 Fixed effects methods
6.11 Bayesian methods
6.12 Summary
       Appendix: Some software and references
7 Assigning values to latent variables
7.1 Introduction
7.2 Posterior distribution
s 7.3 Empirical Bayes (EB)
7.4 Empirical Bayes modal (EBM)
7.5 Maximum likelihood
7.6 Relating the scoring methods in the `linear case'
7.7 Ad hoc scoring methods
7.8 Some uses of latent scoring and classification
7.9 Summary and further reading
      Appendix: Some software
8 Model specification and inference
8.1 Introduction
8.2 Statistical modeling
8.3 Inference (likelihood based)
8.4 Model selection: Relative fit criteria
8.5 Model adequacy: Global absolute fit criteria
8.6 Model diagnostics: Local absolute fit criteria
8.7 Summary and further reading
II Applications
9 Dichotomous responses
9.1 Introduction
9.2 Respiratory infection in children: A random intercept model
9.3 Diagnosis of myocardial infarction: A latent class model
9.4 Arithmetic reasoning: Item response models
9.5 Nicotine gum and smoking cessation: A meta-analysis
9.6 Wives' employment transitions: Markov models with unobserved heterogeneity
9.7 Counting snowshoe hares: Capture-recapture models with heterogeneity
9.8 Attitudes to abortion: A multilevel item response model
9.9 Summary and further reading
10 Ordinal responses
10.1 Introduction
10.2 Cluster randomized trial of sex education: Latent growth curve model
10.3 Political efficacy: Factor dimensionality and item-bias
10.4 Life satisfaction: Ordinal scaled probit factor models
10.5 Summary and further reading
11 Counts
11.1 Introduction
11.2 Prevention of faulty teeth in children: Modeling overdispersion
11.3 Treatment of epilepsy: A random coefficient model
11.4 Lip cancer in Scotland: Disease mapping
11.5 Summary and further reading
12 Durations and survival
12.1 Introduction
12.2 Modeling multiple events clustered duration data
12.3 Onset of smoking: Discrete time frailty models
12.4 Exercise and angina: Proportional hazards random effects and factor models
12.5 Summary and further reading
13 Comparative responses
13.1 Introduction
13.2 Heterogeneity and ‘Independence from Irrelevant Alternatives’
13.3 Model structure
13.4 British general elections: Multilevel models for discrete choice and rankings
13.5 Post-materialism: A latent class model for rankings
13.6 Consumer preferences for coffee makers: A conjoint choice model
13.7 Summary and further reading
14 Multiple processes and mixed responses
14.1 Introduction
14.2 Diet and heart disease: A covariate measurement error model
14.3 Herpes and cervical cancer: A latent class covariate measurement error model for a case-control study
14.4 Job training and depression: A complier average causal effect model
14.5 Physician advice and drinking: An endogenous treatment model
14.6 Treatment of liver cirrhosis: A joint survival and marker model
14.7 Summary and further reading
Author index
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