Robustifying generalized linear mixed models using a new class of mixtures of multivariate Polya trees

Journal of Computational and Graphical Statistics

Volumn 18, Issue 4, 2009, Pages 838-860

  Jara, Alejandro ^a   Hanson, Timothy E ^b   Lesaffre, Emmanuel ^c,d  

^a UNIVERSITY OF CONCEPCIÓN   (Chile)

^b UNIVERSITY OF MINNESOTA   (United States)

^c UNIVERSITY OF LEUVEN   (Belgium)

^d ERASMUS MEDICAL CENTER   (Netherlands)

Author keywords

Bayesian nonparametric; Orthogonal matrix

Indexed keywords

EID: 72449141677     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1198/jcgs.2009.07062     Document Type: Article

References (41)

1. Barron, A., Schervish, M. J., and Wasserman, L. (1999), "Posterior Distributions in Nonparametric Problems," The Annals of Statistics, 27, 536-561.
2. Berger, J. O., and Guglielmi, A. (2001), "Bayesian and Conditional Frequentist Testing of a Parametric Model versus Nonparametric Alternatives," Journal of the American Statistical Association, 96, 174-184.
3. Bush, C. A., and MacEachern, S. N. (1996), "A Semiparametric Bayesian Model for Randomised Block Designs," Biometrika, 83, 275-285.
4. Diggle, P. J., Liang, K.-Y., and Zeger, S. L. (1994), Analysis of Longitudinal Data, New York: Oxford University Press.
5. Escobar, M. D. (1994), "Estimating Normal Means With a Dirichlet Process Prior," Journal of the American Statistical Association, 89, 268-277.
6. Escobar, M. D., and West, M. (1995), "Bayesian Density Estimation and Inference Using Mixtures," Journal of the American Statistical Association, 90, 577-588.
7. Fang, K.-T., Kotz, S., and Ng, K.-W. (1990), Symmetric Multivariate and Related Distributions, New York: Chapman & Hall.
8. Ferguson, T. S. (1973), "A Bayesian Analysis of Some Nonparametric Problems," The Annals of Statistics, 1, 209-230.
9. - (1974), "Prior Distribution on the Spaces of Probability Measures," The Annals of Statistics, 2, 615-629.
10. Ferreira, J. T. A. S., and Steel, M. F. J. (2007), "A New Class of Skewed Multivariate Distributions With Applications to Regression Analysis," Statistica Sinica, 17, 505-529.
11. Gamerman, D. (1997), "Sampling From the Posterior Distribution in Generalized Linear Mixed Models," Statistics and Computing, 7, 57-68.
12. Geisser, S., and Eddy,W. (1979), "A Predictive Approach to Model Selection," Journal of the American Statistical Association, 74, 153-160.
13. Gelfand, A. E., and Dey, D. (1994), "Bayesian Model Choice: Asymptotics and Exact Calculations," Journal of the Royal Statistical Society, Ser. B, 56, 501-514.
14. Gelman, A. (2006), "Prior Distributions for Variance Parameters in Hierarchical Models," Bayesian Analysis, 1, 515-533.
15. Genz, A. (1998), "Methods for Generating Random Orthogonal Matrices," in Monte Carlo and Quasi-Monte Carlo Methods, eds. H. Niederreiter and J. Spanier, Berlin: Springer-Verlag, pp. 199-213.
16. Ghidey, W., Lesaffre, E., and Eilers, P. (2004), "Smooth Random Effects Distribution in a Linear Mixed Model," Biometrics, 60, 945-953.
17. Guha, S. (2008), "Posterior Simulation in the Generalized Linear Mixed Model With Semiparametric Random Effects," Journal of Computational and Graphical Statistics, 17, 410-425.
18. Gupta, A. K., and Nagar, D. K. (1999), Matrix Variate Distributions, New York: Chapman & Hall.
19. Haario, H., Saksman, E., and Tamminen, J. (2001), "An Adaptive Metropolis Algorithm," Bernoulli, 7, 223-242.
20. Halmos, P. R. (1950), Measure Theory, Princeton: Van Nostrand.
21. Hanson, T. (2006), "Inference for Mixtures of Finite Polya Tree Models," Journal of the American Statistical Association, 101, 1548-1565.
22. Hanson, T., and Johnson, W. O. (2002), "Modeling Regression Error With a Mixture of Polya Trees," Journal of the American Statistical Association, 97, 1020-1033.
23. Jara, A. (2007), "Applied Bayesian Non- and Semi-Parametric Inference Using DPpackage," Rnews, 7, 17-26.
24. Kleinman, K. P., and Ibrahim, J. G. (1998a), "A Semi-Parametric Bayesian Approach to Generalized Linear Mixed Models," Statistics in Medicine, 17, 2579-2596.
25. - (1998b), "A Semiparametric Bayesian Approach to the Random Effects Models," Biometrics, 54, 921-938.
26. Lavine, M. (1992), "Some Aspects of Polya Tree Distributions for Statistical Modeling," The Annals of Statistics, 20, 1222-1235.
27. - (1994), "More Aspects of Polya Tree Distributions for Statistical Modeling," The Annals of Statistics, 22, 1161-1176.
28. Mukhopadhyay, S., and Gelfand, A. E. (1997), "Dirichlet Process Mixed Generalized Linear Models," Journal of the American Statistical Association, 92, 633-647.
29. Müller, P., and Quintana, F. A. (2004), "Nonparametric Bayesian Data Analysis," Statistical Science, 19 (1), 95-110.
30. Müller, P., and Rosner, G. L. (1997), "A Bayesian Population Model With Hierarchical Mixture Priors Applied to Blood Count Data," Journal of the American Statistical Association, 92, 1279-1292.
31. Paddock, S. M. (1999), "Randomized Polya Trees: Bayesian Nonparametrics for Multivariate Data Analaysis," unpublished Ph.D. thesis, Duke University, Inistitute of Statistics and Decision Sciences.
32. - (2002), "Bayesian Nonparametric Multiple Imputation of Partially Observed Data With Ignorable Nonresponse," Biometrika, 89, 529-538.
33. Paddock, S. M., Ruggeri, F., Lavine, M., and West, M. (2003), "Randomized Polya Tree Models for Nonparametric Bayesian Inference," Statistica Sinica, 13, 443-460.
34. R Development Core Team (2009), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing, available at http://www.R-project.org.
35. Roberts, G. O., and Rosenthal, J. S. (2006), "Examples of Adaptive MCMC," technical report, Lancaster University, Dept. of Mathematics and Statistics.
36. Spiegelhalter, S. D., Best, N. G., Carlin, B. P., and Van der Linde, A. (2002), "Bayesian Measures of Model Complexity and Fit," Journal of the Royal Statistical Society, Ser. B, 64, 583-639.
37. Stewart, G. W. (1980), "The Efficient Generation of Random Orthogonal Matrices With An Application to Condition Estimators," SIAM Journal on Numerical Analysis, 17, 403-409.
38. Thall, P. F., and Vail, S. C. (1990), "Some Covariance Models for Longitudinal Count DataWith Overdispersion," Biometrics, 46, 657-671.
39. Tierney, L. (1994), "Markov Chains for Exploring Posterior Distributions," The Annals of Statistics, 22, 1701-1762.
40. Walker, S. G., and Mallick, B. K. (1997), "Hierarchical Generalized Linear Models and Frailty Models With Bayesian Nonparametric Mixing," Journal of the Royal Statistical Society, Ser. B, 59, 845-860.
41. Zhang, D., and Davidian, M. (2001), "Linear Mixed Models With Flexible Distributions of Random Effects for Longitudinal Data," Biometrics, 57, 795-802.