Bayesian analysis of longitudinal data using growth curve models

International Journal of Behavioral Development

Volumn 31, Issue 4, 2007, Pages 374-383

  Zhang, Zhiyong ^a   Hamagami, Fumiaki ^a   Wang, Lijuan ^a   Nesselroade, John R ^a   Grimm, Kevin J ^b  

^a UNIVERSITY OF VIRGINIA   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bayesian analysis; Growth curve models; Informative priors; Longitudinal data; Pooling data; WinBUGS

Indexed keywords

ARTICLE; BAYES THEOREM; CHILD DEVELOPMENT; DATA ANALYSIS; DEVELOPMENTAL PSYCHOLOGY; GROWTH CURVE; HUMAN; INFORMATION PROCESSING; LATENT PERIOD; LONGITUDINAL STUDY; MATHEMATICAL COMPUTING; MAXIMUM LIKELIHOOD METHOD; MONTE CARLO METHOD; PROBABILITY; READING; STATISTICAL MODEL;

EID: 34347330128     PISSN: 01650254     EISSN: 14640651     Source Type: Journal    
DOI: 10.1177/0165025407077764     Document Type: Article

References (44)

1. Arminger, G., & Muthen, B.O. (1998). A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the Metropolis-Hastings algorithm. Psychometrika, 63, 271-300.
2. Baltes, P.B., & Nesselroade, J.R. (1979). History and rationale of longitudinal research. In J.R. Nesselroade & P.B. Baltes (Eds.), Longitudinal research in the study of behavior and development (pp. 1-39). New York: Academic Press.
3. Bartholomew, D.J. (1981). Posterior analysis of the factor model. British Journal of Mathematical and Statistical Psychology, 34, 93-99.
4. Blozis, S.A., Conger, K.J., & Harring, J. (2007). Nonlinear latent curve models for multivariate longitudinal data. International Journal of Behavioral Development, 31, 340-346.
5. Box, G.E.P., & Tiao, G.C. (1992). Bayesian inference in statistical analysis. New York: Wiley.
6. Carlin, B.P., & Louis, T.A. (2000). Bayes and empirical Bayes methods for data analysis (2nd ed.). Boca Raton, FL: Chapman and Hall/ CRC.
7. Casella, G., & Berger, R.L. (2001). Statistical inference (2nd ed.). Pacific Grove, CA: Duxbury Press.
8. Chang, H.-H. (1996). The asymptotic posterior normality of the latent trait for polytomous IRT models. Psychometrika, 61, 445-463.
9. Demidenko, E. (2004). Mixed models: Theory and applications. New York: Wiley.
10. Dunson, D. (2003). Dynamic latent trait models for multidimensional longitudinal data. Journal of the American Statistical Association, 98 (463), 555-563.
11. Eaves, L., & Erkanli, A. (2003). Markov Chain Monte Carlo approaches to analysis of genetic and environmental components of human developmental change and G X E interaction. Behavior Genetics, 33, 279-299.
12. Edwards,W., Lindman, H., & Savage, L.J. (1963). Bayesian statistical inference for psychological research. Psychological Review, 70, 193-242.
13. Embretson, S.E., & Reise, S.P. (2000). Item response theory for psychologists. Mahwah, NJ: Erlbaum.
14. Fox, J.-P., & Glas, C.A.W. (2001). Bayesian estimation of a multilevel IRT model using Gibbs sampling. Psychometrika, 66, 271-288.
15. Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
16. Hamagami, F., Zhang, Z., & McArdle, J.J. (submitted). Comparison of parameter estimations of the latent difference score model using structure equation model and Bayesian method.
17. Ibrahim, J.G., & Chen, M.-H. (2000). Power prior distributions for regression models. Statistical Science, 15, 46-60.
18. Laird, N.M., & Ware, J.H. (1982). Random-effects models for longitudinal data. Biometrics, 38, 963-974.
19. Lee, J.C., & Chang, C.H. (2000) Bayesian analysis of a growth curve model with a general autoregressive covariance structure. Scandinavian Journal of Statistics, 27, 703-713.
20. Lee, J.C., Liu, K.-C. (2000) Bayesian analysis of a general growth curve model with predictions using power transformations and AR(1) autoregressive dependence. Journal of Applied Statistics, 27, 321-336.
21. Lee, P.M. (2004). Bayesian statistics: An introduction (3rd ed.). London: Arnold.
22. Lee, S. (1981). A Bayesian approach to confirmatory factor analysis. Psychometrika, 46, 153-160.
23. McArdle, J.J. (1988). Dynamic but structural equation modeling of repeated measures data. In J.R. Nesselroade (pp. R.B. Cattell (Eds.), The handbook of multivariate experimental psychology, 2 (pp. 561-614). New York: Plenum Press.
24. McArdle, J.J. (2001). A latent difference score approach to longitudinal dynamic structural analyses. In R. Cudeck, S. du Toit, (pp. D. Sorbom (Eds.), Structural equation modeling: Present and future (pp. 342-380). Lincolnwood, IL: Scientific Software International.
25. McArdle, J.J., & Epstein, D. (1987). Latent growth curves within developmental structural equation models. Child Development, 58, 110-133.
26. McArdle, J.J., & Hamagami, F. (2001). Latent difference score structural models for linear dynamic analyses with incomplete longitudinal data. In L. Collins & A. Sayer (Eds.), New methods for the analysis of change (pp. 139-175). Washington, DC: American Psychological Association.
27. McArdle, J.J., & Horn, J.L. (2004). A mega analysis of the WAIS: Adult intelligence across the life-span. Mahwah, NJ: Erlbaum.
28. McArdle, J.J., & Nesselroade, J.R. (2003). Growth curve analysis in contemporary psychological research. In J. Schinka & W. Velicer (Eds.), Comprehensive handbook of psychology: Research methods in psychology (Vol. 2, p. 447-480). New York: Wiley.
29. McArdle, J.J., & Wang, L. (in press). Modeling age-based turning points in longitudinal life-span growth curves of cognition. In P. Cohen (Ed.), Turning points research. Mahwah, NJ: Erlbaum.
30. Menzefricke, U. (1998) Bayesian prediction in growth-curve models with correlated errors. Test, 8 (1), 75-93.
31. Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107-122.
32. Pettitt, A.N., Tran, T.T., Haynes, M.A., & Hay, J.L. (2006). A Bayesian hierarchical model for categorical longitudinal data from a social survey of immigrants. Journal of Royal Statistical Society, A, 169, 97-114.
33. Rindskopf, D. (2006, June). Some neglected relationships between cognitive psychology and statistics: How people try to think using advanced statistical methods without realizing it. Paper presented at the 71st Annual Meeting of the Psychometric Society, Montreal, Canada.
34. Rupp, A.A., Dey, D.K., & Zumbo, B.D. (2004). To Bayes or not to Bayes, from whether to when: Applications of Bayesian methodology to modeling. Structural Equation Modeling: A Multidisciplinary Journal, 11, 424-451.
35. Scheines, R., Hoijtink, H., & Boomsma, A. (1999). Bayesian estimation and testing of structural equation models. Psychometrika, 64, 37-52.
36. Seltzer, M.H., Wong, W.H.M., & Bryk, A.S. (1996). Bayesian analysis in applications of hierarchical models: Issues and methods. Journal of Educational Statistics, 21, 131-167.
37. Spiegelhalter, D.J., Best, N.G., Carlin, B.P., & Linde, A. V. D. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64, 583-639.
38. Spiegelhalter, D.J., Thomas, A., Best, N., & Lunn, D. (2003). WinBUGS manual version 1.4. (MRC Biostatistics Unit, Institute of Public Health, Robinson Way, Cambridge CB2 2SR, UK) http://www.mrc-bsu.cam.ac.uk/bugs
39. Tucker, I.R. (1958). Determination of parameters of a functional relation by factor analysis. Psychometrika, 23, 19-23.
40. Walker, L.J., Gustafson, P., & Frimer, J.A. (2007). The application of Bayesian analysis to issues in developmental research. International Journal of Behavioral Development, 31.
41. Wishart, J. (1938). Growth rate determinations in nutrition studies with the bacon pig, and their analyses. Biometrika, 30, 16-28.
42. Wolf, F.M. (1986). Meta-analysis: Quantitative methods for research synthesis. Beverly Hills, CA: SAGE.
43. Zhang, Z., & Wang, L. (2006). BAUW: Bayesian analysis using WinBUGS,Version 1.0. [Computer software and manual]. Available: http://bauw.psychstat.org
44. Zuur, G., Garthwaite, P.H., & Fryer, R.J. (2002). Practical use of MCMC methods: Lessons from a case study. Biometrical Journal, 44, 433-455