Bayesian analysis of hierarchical linear mixed modeling using the multivariate t distribution

Journal of Statistical Planning and Inference

Volumn 137, Issue 2, 2007, Pages 484-495

  Lin, Tsung I ^a   Lee, Jack C ^b  

^a NATIONAL CHUNG HSING UNIVERSITY   (Taiwan)

^b NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

Autoregressive process; Bayesian prediction; Markov chain Monte Carlo; Missing values; Random effects; t linear mixed models

Indexed keywords

EID: 33749325750     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2005.12.010     Document Type: Article

References (31)

1. Barndorff-Nielsen O., and Schou G. On the parameterization of autoregressive models by partial autocorrelations. J. Multivariate Anal. 3 (1973) 408-419
2. Box, G.E.P., Jenkins, G.M., Reinsel, G.C., 1994. Time Series Analysis Forecasting and Control, third ed. Prentice-Hall, Englewood Cliffs, NJ.
3. Brooks S.P., and Gelman A. General methods for monitoring convergence of iterative simulations. J. Comput. Graph. Statist. 7 (1998) 434-455
4. Chi E.M., and Reinsel G.C. Models for longitudinal data with random effects and AR(1) errors. J. Amer. Statist. Assoc. 84 (1989) 452-459
5. Chib S., and Carlin E. On MCMC sampling in hierarchical models. Statist. Comput. 9 (1999) 17-26
6. D'yachkova Y.D., Petkau J., and White R. Longitudinal analysis for magnetic resonance imaging outcomes in multiple sclerosis clinical trials. J. Biopharm. Statist. 7 (1997) 501-531
7. Gelfand A.E., and Smith A.F.M. Sampling based approaches to calculate marginal densities. J. Amer. Statist. Assoc. 85 (1990) 398-409
8. Gelfand A.E., Hills S.E., Racine-Poon A., and Smith A.F.M. Illustration of Bayesian inference in normal data models using Gibbs sampling. J. Amer. Statist. Assoc. 85 (1990) 972-985
9. Gelfand A.E., Smith A.F.M., and Lee T.M. Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling. J. Amer. Statist. Assoc. 85 (1992) 523-532
10. Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B., 2004. Bayesian Data Analysis. second ed. Chapman & Hall, CRC press, London, Boca Raton, FL.
11. Geman S., and Geman D. Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6 (1984) 721-741
12. Gill P.S. A robust mixed linear model analysis for longitudinal data. Statist. Med. 19 (2000) 975-987
13. Hastings W.K. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 (1970) 97-109
14. Keramidas E.M., and Lee J.C. Selection of a covariance structure for growth curves. Biometrical J. 37 (1995) 783-797
15. Laird N.M., and Ware J.H. Random effects models for longitudinal data. Biometrics 38 (1982) 963-974
16. Lange K.L., Little R.J.A., and Taylor J.M.G. Robust statistical modeling using the t distribution. J. Amer. Statist. Assoc. 84 (1989) 881-896
17. Lee J.C. Prediction and estimation of growth curve with special covariance structures. J. Amer. Statist. Assoc. 83 (1988) 432-440
18. Lee J.C., Lin T.I., Lee K.J., and Hsu Y.L. Bayesian analysis of Box-Cox transformed linear mixed models with ARMA (p, q) dependence. J. Statist. Plann. Inference. 133 (2005) 435-451
19. Lin T.I., and Lee J.C. On modeling data from degradation sample paths over time. Austral. J. Statist. 45 (2003) 257-270
20. Lin, T.I., Lee, J.C., 2006. A robust approach to t linear mixed models applied to multiple sclerosis data. Statist. Med., to appear.
21. Little R.J.A., and Rubin D.B. Statistical Analysis With Missing Data. second ed. (2002), Wiley, New York
22. Liu C.H., and Rubin D.B. Ellipsoidally symmetric extensions of the general location model for mixed categorical and continuous data. Biometrika 85 (1998) 673-688
23. Newton M.A., and Raftery A.E. Approximate Bayesian inference by the weighted likelihood bootstrap (with discussion). J. Roy. Statist. Soc. B 56 (1994) 3-48
24. Pinheiro J.C., Liu C.H., and Wu Y.N. Efficient algorithms for robust estimation in linear mixed-effects models using the multivariate t distribution. J. Comput. Graph. Statist. 10 (2001) 249-276
25. Rao C.R. Prediction of future observations in growth curve models. Statist. Sci. 2 (1987) 434-471
26. Rochon J. ARMA covariance structures with time heteroscedasticity for repeated measures experiments. J. Amer. Statist. Assoc. 87 (1992) 777-784
27. Rubin D.B. Inference and missing data. Biometrika 63 (1976) 581-592
28. Schafer J.L., and Yucel R.M. Computational strategies for multivariate linear mixed-effects models with missing values. J. Comput. Graph. Statist. 11 (2002) 437-457
29. Wakefield J.C., Smith A.F.M., Racine-Poon A., and Gelfand A.E. Bayesian analysis of linear and non-linear model by using Gibbs sampler. Appl. Statist. 43 (1994) 201-221
30. Zeger S.L., and Karim M.R. Generalized linear models with random effects; a Gibbs sampling approach. J. Amer. Statist. Assoc. 86 (1991) 79-86
31. Zellner A. Bayesian and non-Bayesian analysis of the regression model with multivariate student-t error terms. J. Amer. Statist. Assoc. 71 (1976) 400-405