A simulation study comparison of bayesian estimation with conventional methods for estimating unknown change points

Structural Equation Modeling

Volumn 15, Issue 1, 2008, Pages 52-74

  Wang, Lijuan ^a   McArdle, John J ^b  

^a UNIVERSITY OF VIRGINIA   (United States)

^b UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BAYESIAN APPROACHES; BAYESIAN ESTIMATIONS; CONVENTIONAL METHODS; COVARIANCE PARAMETERS; GAUSSIAN QUADRATURES; LONGITUDINAL DATA; SIMULATION STUDIES; TAYLOR EXPANSION METHOD;

COMPUTER SIMULATION; ESTIMATION; MONTE CARLO METHODS; NUMERICAL ANALYSIS; NUMERICAL METHODS;

BAYESIAN NETWORKS;

EID: 41149108683     PISSN: 10705511     EISSN: None     Source Type: Journal    
DOI: 10.1080/10705510701758265     Document Type: Article

References (47)

1. Beal, S. L., & Sheiner, L. B. (1982). Estimating population kinetics. CRC Critical Reviews in Biomedical Engineering, 8, 195-222.
2. Bennett, J. E., Racine-Poon, A., & Wakefield, J. C. (1996). MCMC for nonlinear hierarchical models. In W. R. Gilks, S. Richardson, & D. J. Spiegelhalter (Eds.), Markov chain Monte Carlo in practice (pp. 339-357). London: Chapman & Hall.
3. Blozis, S. A. (2004). Structural latent curve models for the study of change in multivariate repeated measures. Psychological Methods, 9, 334-353.
4. Bock, R. D., & Thissen, D. (1980). Statistical problems of fitting curves for individual growth in stature. In E. F. Johnson, A. F. Roche, & C. Susanne (Eds.), Human physical growth and development: Methodologies & factors (pp. 265-290). New York: Plenum.
5. Bock, R. D., Wainer, H., Peterson, A., Thissen, D., Murray, J., & Roche, A. (1973). A parameterization for .individual human growth curves. Human Biology, 45, 63-80.
6. Brooks, S. P., & Roberts, G. O. (1998). Assessing convergence of Markov Chain Monte Carlo algorithms, Statistics and Computing, 8, 319-335.
7. Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical linear models. Newbury Park, CA: Sage.
8. Carlin, B. P., & Louis, T. A. (2000). Bayes and empirical Bayes methods for data analysis (2nd ed.). Boca Raton, FL: Chapman & Hall/CRC.
9. Chib, S., & Greenberg, E. (1995). Understanding the Metropolis-Hastings algorithm. The American Statistician, 49, 327-335.
10. Congdon, P. (2001). Bayesian statistical modeling. New York: Wiley.
11. Congdon, P. (2003). Applied Bayesian modeling. New York: Wiley.
12. Cudeck, R., & Du Toit, S. H. C. (2003). Nonlinear multilevel models for repeated measures data. In S. P. Reise & N. Duan (Eds.), Multilevel modeling: Methodological advances, issues, and applications (pp. 1-24). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
13. Cudeck, R., & Klebe, K. J. (2002). Multiphase mixed-effects model for repeated measure data. Psychological Methods, 7 (1), 41-63.
14. Curran, P. J. (2003). Have multilevel models been structural equation models all along? Multivariate Behavioral Research, 38, 529-569.
15. Davidian, M., & Giltinan, D. M. (1995). Nonlinear models for repeated measurement data. London: Chapman & Hall.
16. Davidian, M., & Giltinan, D. M. (2003). Nonlinear models for repeated measurements: An overview and update. Editor's invited paper. Journal of Agricultural, Biological, and Environmental Statistics, 8, 387-419.
17. Diggle, P. J., Liang, K.-Y., & Zeger, S. L. (1994). Analysis of longitudinal data. Oxford, UK: Oxford University Press.
18. Evans, B. A., Feng, Z., & Peterson, A. V. (2001). A comparison of generalized linear mixed model procedures with estimating equations for variance and covariance parameter estimation in longitudinal studies and group randomized trials. Statistics in Medicine, 20, 3353-3373.
19. Ferrer, E., Hainagami, F., & McArdle, J. J. (2004). Modeling latent growth curves with incomplete data using different types of structural equation modeling and multilevel software. Structural Equation Modeling, 11, 452-483.
20. Gallant, A. R., & Fuller, W. A. (1973). Fitting segmented polynomial regression models whose join points have to be estimated. Journal of the American Statistical Association, 68, 144-147.
21. Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
22. Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In J. M. Bernardo, A. F. M. Smith, A. P. Dawid, & J. O. Berger (Eds.), Bayesian statistics 4 (pp. 169-193). New York: Oxford University Press.
23. Gilks, W. R., Richardson, S., & Spiegelhalter, D. J. (1996). Introducing Markov chain Monte Carlo. In W. R. Gilks, S. Richardson, & D. J. Spiegelhalter (Eds.), Markov chain Monte Carlo in practice (pp. 339-357). London: Chapman. & Hall.
24. Hall, C. B., Lipton, R., Sliwinski, M., & Stewart, W. F. (2000). A change point model for estimating the onset of cognitive decline in preclinical Alzheimer's disease. Statistics in Medicine, 19, 1555-1566.
25. Hall, C. B., Ying, J., Kuo, L., Sliwinski, M., Buschke, H., Katz, M., et al. (2001). Estimation of bivariate measurements having different change points, with application to cognitive ageing. Statistics in Medicine, 20, 3695-3714.
26. Ibrahim, J. G., & Chen, M.-H. (2000). Power prior distributions for regression models. Statistical Science, 15(1), 46-60.
27. Laird, N., & Ware, J. (1982). Random-effects model for longitudinal data. Biometrics, 38, 963-974.
28. Lindstrom, M. J., & Bates, D. M. (1990). Nonlinear mixed effects models for repeated measures. Biometrics, 46, 673-687.
29. Little, R. C., Milliken, G. A., Stroup, W. W., & Wolfinger, R. D. (1996). SAS system for mixed models. Cary, NC: SAS Institute.
30. McArdle, J. J. (2006). Dynamic structural equation modeling in longitudinal experimental studies. In K. van Montfort, J. Oud, & A. Satorra et al. (Eds.), Longitudinal models in the behavioral and related sciences (pp. 159-188). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
31. McArdle, J. J., Ferrer-Caja, E., Hainagami, F., & Woodcock, R.W. (2002). Comparative longitudinal multilevel structural, analyses of the growth and decline of multiple intellectual abilities over the life-span. Developmental Psychology, 38, 115-142.
32. McArdle, J. J., & Hamagami, E. (1992). Modeling incomplete longitudinal and cross-sectional data using latent growth structural models. Experimental Aging Research, 18, 145-166.
33. McArdle, J. J., & Nesselroade, J. R. (2003). Growth curve analyses in contemporary psychological research. In J. Schinka & W. Velicer (Eds.), Comprehensive handbook of psychology: Vol. 2: Research methods in psychology (pp. 447-480). New York: Pergamon.
34. 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: Lawrence Erlbaum Associates, Inc.
35. Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107-122.
36. Morrell, C. H., Pearson, J. D., Carter, H. B., & Brant, L. J. (1995). Estimating unknown transition times using piecewise nonlinear mixed-effects model in men with prostate cancer. Journal of the American Statistical Association, 90, 45-53.
37. Pan, J.-X., & Fang, K.-T. (2002). Growth curve models and statistical diagnostics. New York: Springer.
38. Pinheiro, J. C., & Bates, D. M. (1995). Approximations to the log-likelihood function in the nonlinear mixed-effects model. Journal of Computational and Graphical Statistics, 4, 12-35.
39. Plummer, M., Best, N., Cowles, K., & Vines, K. (2005). Output analysis and diagnostics for MCMC. Retrieved December 1, 2005, from http://www-fis.iarc.fr/coda/
40. Seltzer, M., Wong, W. H., & Bryk, A. (1996). Bayesian inference in application of hierarchical models: Issues and methods. Journal of Education and Behavioral Statistics, 21, 131-167.
41. Smith, A. F. M., & Cook, D. G. (1980). Straight lines with a change-point: A Bayesian analysis of some renal transplant data. Applied Statistics, 29, 180-189.
42. Spiegelhalter, D., Thomas, A., Best, N., & Lunn, D. (2003). WinBUGS manual [version 1.4.1]. Cambridge, UK: MRC Biostatistics Unit, Cambridge University. Retrieved November 1, 2004, from http://www.mrc-bsu.cam. ac.uk/bugs/welcome.shtml
43. Verbeke, G., & Molenberghs, G. (2000). Linear mixed models for longitudinal data. New York: Springer.
44. Vonesh, E. F. (1996). A note on the use of Laplace's approximation for nonlinear mixed-effects models. Biometrika, 83, 447-452.
45. Wolfinger, R. D. (1993). Laplace's approximation for nonlinear mixed models, Biometrika, 80, 791-795.
46. Wolfinger, R. D. (1999). Fitting nonlinear mixed models with the new NLMIXED procedure (Tech. Paper No. 287). Cary, NC: SAS Institute.
47. Zhang, Z., Hamagami, F., Wang, L., Grimm, K. J., & Nesselroade, J. R. (2007). Bayesian analysis of longitudinal data using growth curve models. International Journal of Behavioral Research, 31, 374-383.