Difficulties in Drawing Inferences With Finite-Mixture Models

American Statistician

Volumn 58, Issue 2, 2004, Pages 152-158

  Chung, Hwan ^a   Loken, Eric ^b   Schafer, Joseph L ^c  

^a Research Associate of The Methodology Center   (United States)

^b Human Development and Family Studies   (United States)

^c PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

EM algorithm; Label switching; Markov chain Monte Carlo

Indexed keywords

EID: 2442480804     PISSN: 00031305     EISSN: 15372731     Source Type: Journal    
DOI: 10.1198/0003130043286     Document Type: Article

References (20)

1. Aitkin, M., and Rubin, D. B. (1985), “Estimation and Hypothesis Testing in Finite Mixture Models,” Journal of the Royal Statistical Society, Series B,47, 67-75.
2. Brooks, S. P. (1998), “Markov Chain Monte Carlo Method and its Application,” The Statistician, 44, 69-100.
3. Celeux, G. (1998),“Bayesian Inference for Mixture: The Label-Switching Prob-lem,” in Compstat98, eds. R. Payne and P. Green, Heidelberg: Physica, pp. 227-232.
4. Celeux, G., Hurn, M., and Robert, C. P. (2000), “Computational and Inferential Difficulties With Mixture Posterior Distributions,” Journal of the American Statistical Association, 95, 957-970.
5. Chung, H. (2003), “Latent-Class Modeling with Covariates,” doctoral dissertation, The Pennsylvania State University, University Park.
6. Cowles, M. K., and Carlin, B. P. (1996), “Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review,” Journal of the American Statistical Association, 91, 883-904.
7. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977), “MaximumLikelihood Estimation From Incomplete Data via the EM Algorithm” (with discussion), Journal of the Royal Statistical Society, Series B, 39, 1-38.
8. Goodman, L. A. (1974), “Exploratory Latent Structure Analysis Using Both Identifiable and Unidentifiable Models,” Biometrika, 61, 215-231.
9. Gelfand, A. E., and Smith, A. F. M. (1990), “Sampling-Based Approaches to Calculating Marginal Densities,” Journal of the American Statistical Associ-ation, 85, 398-409.
10. Little, R. J. A., and Rubin, D. B. (1987), StatisticalAnalysis with Missing Data, New York: Wiley.
11. Loken, E. (in press), “Multi-Modality in Mixture Models and Latent Trait Models,” in Missing Data and Bayesian Methods in Practice: Contributions by Donald Rubin’s Statistical Family, eds. A. Gelman and X. Meng, New York: Wiley.
12. McLachlan, G., and Krishnan, T. (1997), The EM Algorithm and Expectations, New York: Wiley.
13. McLachlan, G., and Peel, D. (2000), Finite Mixture Models, New York:Wiley.
14. Richardson, S., and Green, P. J. (1997), “On Bayesian Analysis of Mixtures With an Unknown Number of Components,” Journal of the Royal Statistical Society, Series B, 59, 731-792.
15. Robert, C. P. (1996), “Mixtures of Distributions: Inference and Estimation,” in Markov Chain Monte Carlo in Practice, eds. W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, London:Chapman & Hall, pp. 441-64.
16. Seidel, W., Mosler, K., and Alker, M. (2000), “Likelihood Ratio Tests Based on Subglobal Optimization: A Power Comparison in Exponential Mixture Models,” Statistical Papers, 41, 85-98.
17. Stephens, M. (1997), “Bayesian Methods for Mixtures of NormalDistributions,” Ph.D. dissertation, Oxford: Magdalen College.
18. Stephens, M. (2000), “Dealing With Label Switching in Mixture Models,” Journal of the Royal Statistical Society, Series B, 62, 795-809.
19. Tanner, M. A., and Wong, W. H. (1987), “The Calculation of Posterior Distributions by Data Augmentation” (with discussion), Journal of the American Statistical Association, 82, 528-550.
20. Titterington, D. M., Smith, A. F. M., and Makov, U. E. (1985), Statistical Analysis of Finite Mixture Distributions, New York: Wiley.