Abstract
This chapter provides a survey of the development of latent variable models that are suitable for analyzing unbalanced longitudinal data. This chapter begins with an introduction, in which the marginal modeling approach (without the use of latent variable) for correlated responses such as repeatedly measured longitudinal data is described. The concepts of random effects and latent variables are introduced at the beginning of Sect. 41.1. Section 41.1.1 describes the linear mixed models of Laird and Ware for continuous longitudinal response; Sect. 41.1.2 discusses generalized linear mixed models (with latent variables) for categorical response; and Sect. 41.1.3 covers models with multilevel latent variables. Section 41.2.1 presents an extended linear mixed model of Laird and Ware for multidimensional longitudinal responses of different types. Section 41.2.2 covers measurement error models for multiple longitudinal responses. Section 41.3 describes linear mixed models with latent class variables—the latent class mixed model that can be useful for either a single or multiple longitudinal responses. Section 41.4 studies the relationships between multiple longitudinal responses through structural equation models.
Section 41.5 unifies all the above varieties of latent variable models under a single multilevel latent variable model formulation.
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Abbreviations
- EM:
-
expectation maximization
- GEE:
-
generalized estimating equation
- GLM:
-
generalized linear model
- GLMM:
-
generalized linear mixed model
- NPC:
-
nutritional prevention of cancer
- SEM:
-
structural equation models
References
N. M. Laird, J. H. Ware: Random-effects models for longitudinal data, Biometrics 38, 963–974 (1982)
P. J. Digglel, P. Heagerty, K.-Y. Liang, S. L. Zeger: Analysis of Longitudinal Data, 2nd edn. (Oxford Univ. Press, Oxford 2002)
K.-Y. Y. Liang, S. L. Zeger: Longitudinal data analysis using generalized linear models, Biometrika 73, 13–22 (1986)
S. Rabe-Hesketh, A. Skrondal, A. Pickles: GLLAMM Manual, U.C. Berkeley Division of Biostatistics Working Paper Series, Vol. 160 ( 2004) http://www.gllamm.org
D. A. Harville, R. W. Mee: A mixed-model procedure for analyzing ordered categorical data, Biometrics 40, 393–408 (1984)
J. Catalano P.: Bivariate modelling of clustered continuous and ordered categorical outcomes, Stat. Med. 16, 883–900 (1997)
C. E. McCulloch, S. R. Searle: Generalized, Linear, and Mixed Models (Wiley, New York 2001)
T. E. Duncan, S. C. Duncan, H. Okut, L. A. Strycker, F. Li: An extension of the general latent variable growth modeling framework to four levels of the hierarchy, Struct. Equ. Model. 9(3), 303–326 (2002)
A. Skrondal, S. Rabe-Hesketh: Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equation Models (Chapman Hall/CRC, New York 2004)
H. Q. Lin, C. E. McCulloch, S. T. Mayne: Maximum likelihood estimation in the joint analysis of time-to-event and multiple longitudinal variables, Stat. Med. 21, 2369–2382 (2002)
S. T. Mayne, B. Cartmel, M. Baum, G. Shor-Posner, B. G. Fallon, K. Briskin, J. Bean, T. Z. Zheng, D. Cooper, C. Friedman, W. J. Goodwin: Randomized trial of supplemental beta-carotene to prevent second head and neck cancer, Cancer Res. 61, 1457–1463 (2001)
J. Roy: Latent variable models for longitudinal data with multiple continuous outcomes, Biometrics 56, 1047–1054 (2000)
H. Q. Lin, B. W. Turnbull, C. E. McCulloch, E. H. Slate: Latent class models for joint analysis of longitudinal biomarker and event process data: Application to longitudinal prostate-specific antigen readings and prostate cancer, J. Am. Stat. Assoc. 97, 53–65 (2002)
C. E. McCulloch, H. Lin, E. H. Slate, B. W. Turnbull: Discovering subpopulation structure with latent class mixed models, Stat. Med. 21, 417–429 (2002)
L. C. Clark, G. F. Combs Jr., B. W. Turnbull, E. H. Slate, D. K. Chalker, J. Chow, L. S. Davis, R. A. Glover, G. F. Graham, E. G. Gross, A. Krongrad, J. L. Lesher, H. K. Park, B. B. Sanders, C. L. Smith, J. R. Taylor: Effects of selenium supplementation for cancer prevention in patients with carcinoma of the skin, J. Am. Med. Assoc. 276, 1957–1963 (1996)
L. C. Clark, B. Dalkin, A. Krongrad, G. F. Combs Jr., B. W. Turnbull, E. H. Slate, R. Witherington, J. H. Herlong, E. Janosko, D. Carpenter, C. Borosso, S. Falk, J. Rounder: Decreased incidence of prostate cancer with selenium supplementation: results of a double-blind cancer prevention trial, Brit. J. Urol. 81, 730–734 (1998)
J. J. McArdle: A latent difference score approach to longitudinal dynamic analysis. In: Structural Equation Modeling: Present and Future, ed. by R. Cudeck, S. DuToit, D. Sörbom (Scientific Software International, Lincolnwood, IL 2001) pp. 341–380
J. J. McArdle, E. Ferrer-Caja, F. Hamagami, R. W. Woodcock: Comparative longitudinal structural analyses of the growth and decline of multiple intellectual abilities over the life span, Devel. Psychol. 38, 115–142 (2002)
D. L. Frosch, J. A. Stein, S. Shoptaw: Use latent-variable models to analyze smoking cessation clinical trial data: an example among the methadone maintained, Exp. Clin. Psychopharmacol. 10, 258–267 (2002)
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© 2006 Springer-Verlag
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Lin, H. (2006). Latent Variable Models for Longitudinal Data with Flexible Measurement Schedule. In: Pham, H. (eds) Springer Handbook of Engineering Statistics. Springer Handbooks. Springer, London. https://doi.org/10.1007/978-1-84628-288-1_41
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DOI: https://doi.org/10.1007/978-1-84628-288-1_41
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