Ellipsoidally symmetric extensions of the general location model for mixed categorical and continuous data

Biometrika

Volumn 85, Issue 3, 1998, Pages 673-688

  Liu, Chuanhai ^a   Rubin, Donald B ^b  

^a LUCENT TECHNOLOGIES   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

Em algorithm; Gibbs sampler; Iterative proportional fitting; Maximum likelihood estimation; Multivariate t

Indexed keywords

EID: 0000622671     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/85.3.673     Document Type: Article

References (30)

1. BARTLETT, M. S. (1933). On the theory of statistical regression. Proc. R. Soc. Edin. 53, 260-83.
2. BISHOP, Y. M. M., FIENBERG, S. E. & HOLLAND, P. W. (1975). Discrete Multivariate Analysis: Theory and Practice. Cambridge, MA: MIT Press.
3. DEMPSTER, A. P., LAIRD, N. M. & RUBIN, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with Discussion). J. R. Statist. Soc. B 39, 1-38.
4. GELFAND, A. E. & SMITH, A. F. M. (1990). Sampling based approaches to calculating marginal densities. J. Am. Statist. Assoc. 85, 398-409.
5. GELMAN, A., CARLIN, J. B., STERN, H. S. & RUBIN, D. B. (1995). Bayesian Data Analysis. London: Chapman & Hall.
6. GELMAN, A. & RUBIN, D. B. (1992). Inference from iterative simulation using multiple sequences (with Discussion). Statist. Sei. 7, 457-511.
7. GEMAN, S. & GEMAN, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pat. Anal. Mach. Intel. 6, 721-41.
8. KRZANOWSKI, W. J. (1980). Mixtures of continuous and categorical variables in discriminant analysis. Biometrics 36, 493-9.
9. KRZANOWSKI, W. J. (1982). Mixtures of continuous and categorical variables in discriminant analysis: a hypothesis-testing approach. Biometrics 38, 991-1002.
10. LANGE, K. L., LITTLE, R. J. A. & TAYLOR, J. M. G. (1989). Robust statistical modeling use the t distribution. J. Am. Statist. Assoc. 84, 881-96.
11. LITTLE, R. J. A. (1988). Robust estimation of the mean and covariance matrix from data with missing values. Appl. Statist. 37, 23-39
12. LITTLE, R. J. A. & RUBIN, D. B. (1987). Statistical Analysis with Missing Data. New York: Wiley.
13. LITTLE, R. J. A. & SCHLUCHTER, M. D. (1985). Maximum likelihood estimation for mixed continuous and categorical data with missing values. Biometrika 72, 497-512.
14. Liu, C. (1993). Bartlett's decomposition of the posterior distribution of the covariance for normal monotone ignorable missing data. J. Mult. Anal. 46, 198-206
15. Liu, C. (1995). Missing data imputation using the multivariate t distribution. J. Mult. Anal 53, 139-58.
16. Liu, C. (1996). Bayesian robust multivariate linear regression with incomplete data. J. Am. Statist. Assoc. 91, 1219-27.
17. Liu, C. & RUBIN, D. B. (1994). The ECME algorithm: A simple extension of EM and ECM with faster monotone convergence. Biometrika 81, 633-48.
18. Liu, C. & RUBIN, D. B. (1995). ML estimation of the multivariate t distribution with unknown degrees of freedom. Statist. Sinica 5, 19-39.
19. MENG, X. L. & RUBIN, D. B. (1993). Maximum likelihood estimation via the ECM algorithm: A general framework. Biometrika 80, 267-78.
20. MENG, X. L. & VAN DYK, D. (1997). The EM algorithm-an old folk song sung to a fast new tune (with Discussion). J. R. Statist. Soc. B 59, 511-67.
21. OLKIN, I. & TäTE, R. F. (1961). Multivariate correlation models with discrete and continuous variables. Ann. Math. Statist. 32, 448-65.
22. RITTER, C. & TANNER, M. (1992). Facilitating the Gibbs sampler: The Gibbs stopper and the Griddy-Gibbs sampler. J. Am. Statist. Assoc. 87, 861-8
23. RUBIN, D. B. (1976). Inference and missing data. Biometrika 63, 581-92.
24. RUBIN, D. B. (1983). Iteratively reweighted least squares. In Encyclopedia of Statistical Sciences, 4, Ed. S. Kotz, N. L. Johnson and C. B. Read, pp. 272-5. New York: John Wiley.
25. RUBIN, D. B. (1992). Computational aspects of analyzing random effects/longitudinal models. Statist. Med. 11, 1809-21.
26. RUBIN, D. B. & SCHAFER, J. L. (1990). Efficiently creating multiple imputations for incomplete multivariate normal data. In Proc. Statist. Comp. Sect., pp. 83-8. Washington, DC: Am. Statist. Assoc.
27. RUBIN, D. B. & THOMAS, N. (1992). Affinely invariant matching methods with ellipsoidal distributions. Ann. Statist. 20, 1079-93.
28. SCHAFER, J. L. (1997). Analysis by Simulation of Incomplete Mtiltivariate Data: Algorithms and Examples. New York: Chapman and Hall.
29. TANNER, M. A. & WONG, W. H. (1987). The calculation of posterior distribution by data augmentation (with Discussion). J. Am. Statist. Assoc. 82, 528-50.
30. ZEGER, S. L. & KARIM, M. R. (1991). Generalized linear models with random effects; A Gibbs sampling approach. J. Am. Statist. Assoc. 86, 79-86.