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

by Skrondal; Anders

• ISBN13: 9781584880004
• ISBN10: 1584880007
• Edition: 1st
• Format: Hardcover
• Copyright: 2004-05-11
• Publisher: Chapman & Hall/

Summary

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, a wide range of estimation and prediction methods from biostatistics, psychometrics, econometrics, and statistics are explained and contrasted in a simple way. Exciting and realistic applications demonstrate how researchers can use latent variable modeling to solve concrete problems in areas as diverse as medicine, economics, and psychology. Many nonstandard response types are considered including 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.Contact Editor: CalverOTI #1: C1830

Author Biography

Sophia Rabe-Hesketh is a Professor in the area of Educational Statistics at the Graduate School of Education, University of California, Berkeley, USA.

Table of Contents

Preface	ix
Dedication	xi
I Methodology	xiii
1 The omni-presence of latent variables	1	(20)
1.1 Introduction	1	(1)
1.2 'True' variable measured with error	2	(2)
1.3 Hypothetical constructs	4	(5)
1.4 Unobserved heterogeneity	9	(5)
1.5 Missing values and counterfactuals	14	(2)
1.6 Latent responses	16	(1)
1.7 Generating flexible distributions	17	(1)
1.8 Combining information	18	(1)
1.9 Summary	18	(3)
2 Modeling different response processes	21	(28)
2.1 Introduction	21	(1)
2.2 Generalized linear models	22	(5)
2.3 Extensions of generalized linear models	27	(6)
2.4 Latent response formulation	33	(6)
2.5 Modeling durations or survival	39	(7)
2.6 Summary and further reading	46	(3)
3 Classical latent variable models	49	(46)
3.1 Introduction	49	(1)
3.2 Multilevel regression models	49	(14)
3.3 Factor models and item response models	63	(11)
3.4 Latent class models	74	(1)
3.5 Structural equation models with latent variables	75	(5)
3.6 Longitudinal models	80	(13)
3.7 Summary and further reading	93	(2)
4 General model framework	95	(40)
4.1 Introduction	95	(1)
4.2 Response model	96	(12)
4.3 Structural model for the latent variables	108	(4)
4.4 Distribution of the disturbances	112	(5)
4.5 Parameter restrictions and fundamental parameters	117	(3)
4.6 Reduced form of the latent variables and linear predictor	120	(1)
4.7 Moment structure of the latent variables	121	(2)
4.8 Marginal moment structure of observed and latent responses	123	(4)
4.9 Reduced form distribution and likelihood	127	(3)
4.10 Reduced form parameters	130	(2)
4.11 Summary and further reading	132	(3)
5 Identification and equivalence	135	(24)
5.1 Introduction	135	(1)
5.2 Identification	136	(16)
5.3 Equivalence	152	(5)
5.4 Summary and further reading	157	(2)
6 Estimation	159	(62)
6.1 Introduction	159	(1)
6.2 Maximum likelihood: Closed form marginal likelihood	160	(1)
6.3 Maximum likelihood: Approximate marginal likelihood	161	(13)
6.4 Maximizing the likelihood	174	(8)
6.5 Nonparametric maximum likelihood estimation	182	(2)
6.6 Restricted/Residual maximum likelihood (REML)	184	(1)
6.7 Limited information methods	185	(6)
6.8 Maximum quasi-likelihood	191	(6)
6.9 Generalized Estimating Equations (GEE)	197	(3)
6.10 Fixed effects methods	200	(4)
6.11 Bayesian methods	204	(10)
6.12 Summary	214	(2)
Appendix: Some software and references	216	(5)
7 Assigning values to latent variables	221	(30)
7.1 Introduction	221	(1)
7.2 Posterior distributions	222	(3)
7.3 Empirical Bayes (EB)	225	(10)
7.4 Empirical Bayes modal (EBM)	235	(2)
7.5 Maximum likelihood	237	(4)
7.6 Relating the scoring methods in the 'linear case'	241	(1)
7.7 Ad hoc scoring methods	241	(2)
7.8 Some uses of latent scoring and classification	243	(4)
7.9 Summary and further reading	247	(2)
Appendix: Some software	249	(2)
8 Model specification and inference	251	(32)
8.1 Introduction	251	(1)
8.2 Statistical modeling	251	(6)
8.3 Inference (likelihood based)	257	(5)
8.4 Model selection: Relative fit criteria	262	(5)
8.5 Model adequacy: Global absolute fit criteria	267	(5)
8.6 Model diagnostics: Local absolute fit criteria	272	(8)
8.7 Summary and further reading	280	(3)
II Applications	283	(162)
9 Dichotomous responses	285	(36)
9.1 Introduction	285	(1)
9.2 Respiratory infection in children: A random intercept model	285	(3)
9.3 Diagnosis of myocardial infarction: A latent class model	288	(4)
9.4 Arithmetic reasoning: Item response models	292	(7)
9.5 Nicotine gum and smoking cessation: A meta-analysis	299	(8)
9.6 Wives' employment transitions: Markov models with unobserved heterogeneity	307	(4)
9.7 Counting snowshoe hares: Capture-recapture models with heterogeneity	311	(4)
9.8 Attitudes to abortion: A multilevel item response model	315	(3)
9.9 Summary and further reading	318	(3)
10 Ordinal responses	321	(28)
10.1 Introduction	321	(1)
10.2 Cluster randomized trial of sex education: Latent growth curve model	321	(5)
10.3 Political efficacy: Factor dimensionality and item-bias	326	(12)
10.4 Life satisfaction: Ordinal scaled probit factor models	338	(9)
10.5 Summary and further reading	347	(2)
11 Counts	349	(24)
11.1 Introduction	349	(1)
11.2 Prevention of faulty teeth in children: Modeling overdispersion	349	(6)
11.3 Treatment of epilepsy: A random coefficient model	355	(6)
11.4 Lip cancer in Scotland: Disease mapping	361	(9)
11.5 Summary and further reading	370	(3)
12 Durations and survival	373	(20)
12.1 Introduction	373	(1)
12.2 Modeling multiple events clustered duration data	373	(2)
12.3 Onset of smoking: Discrete time frailty models	375	(7)
12.4 Exercise and angina: Proportional hazards random effects and factor models	382	(8)
12.5 Summary and further reading	390	(3)
13 Comparative responses	393	(24)
13.1 Introduction	393	(1)
13.2 Heterogeneity and 'Independence from Irrelevant Alternatives'	393	(2)
13.3 Model structure	395	(2)
13.4 British general elections: Multilevel models for discrete choice and rankings	397	(7)
13.5 Post-materialism: A latent class model for rankings	404	(4)
13.6 Consumer preferences for coffee makers: A conjoint choice model	408	(7)
13.7 Summary and further reading	415	(2)
14 Multiple processes and mixed responses	417	(28)
14.1 Introduction	417	(1)
14.2 Diet and heart disease: A covariate measurement error model	417	(5)
14.3 Herpes and cervical cancer: A latent class covariate measurement error model for a case-control study	422	(5)
14.4 Job training and depression: A complier average causal effect model	427	(5)
14.5 Physician advice and drinking: An endogenous treatment model	432	(6)
14.6 Treatment of liver cirrhosis: A joint survival and marker model	438	(5)
14.7 Summary and further reading	443	(2)
References	445	(42)
Index	487	(9)
Author index	496