The FMM Procedure

References

  • Aldrich, J. (1997), “R. A. Fisher and the Making of Maximum Likelihood 1912–1922,” Statistical Science, 12(3), 162–176.

  • Breslow, N. E. (1984), “Extra-Poisson Variation in Log-Linear Models,” Applied Statistics, 33, 38–44.

  • Cameron, A. C. and Trivedi, P. K. (1998), Regression Analysis of Count Data, Cambridge: Cambridge University Press.

  • Celeux, G., Forbes, F., Robert, C. P., and Titterington, D. M. (2006), “Deviance Information Criteria for Missing Data Models,” Bayesian Analysis, 1(4), 651–674.

  • Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977), “Maximum Likelihood from Incomplete Data via the EM Algorithm,” Journal of the Royal Statistical Society, Series B, 39, 1–38.

  • Everitt, B. S. and Hand, D. J. (1981), Finite Mixture Distributions, Chapman & Hall.

  • Ferrari, S. L. P. and Cribari-Neto, F. (2004), “Beta Regression for Modelling Rates and Proportions,” Journal of Applied Statistics, 31, 799–815.

  • Fisher, R. A. (1921), “On the 'Probable Error' of a Coefficient of Correlation Deduced from a Small Sample,” Metron, 1, 3–32.

  • Frühwirth-Schnatter, S. (2006), Finite Mixture and Markov Switching Models, New York: Springer.

  • Gamerman, D. (1997), “Sampling from the Posterior Distribution in Generalized Linear Models,” Statistics and Computing, 7, 57–68.

  • Geweke, J. (1992), “Evaluating the Accuracy of Sampling-Based Approaches to Calculating Posterior Moments,” in J. M. Bernardo, J. O. Berger, A. P. Dawiv, and A. F. M. Smith, eds., Bayesian Statistics, volume 4, Oxford, UK: Clarendon Press.

  • Griffiths, D. A. (1973), “Maximum Likelihood Estimation for the Beta-Binomial Distribution and an Application to the Household Distribution of the Total Number of Cases of a Disease,” Biometrics, 29, 637–648.

  • Haseman, J. K. and Kupper, L. L. (1979), “Analysis of Dichotomous Response Data from Certain Toxicological Experiments,” Biometrics, 35, 281–293.

  • Joe, H. and Zhu, R. (2005), “Generalized Poisson Distribution: The Property of Mixture of Poisson and Comparison with Negative Binomial Distribution,” Biometrical Journal, 47, 219–229.

  • Kass, R. E., Carlin, B. P., Gelman, A., and Neal, R. (1998), “Markov Chain Monte Carlo in Practice: A Roundtable Discussion,” The American Statistician, 52, 93–100.

  • Lawless, J. F. (1987), “Negative Binomial and Mixed Poisson Regression,” The Canadian Journal of Statistics, 15, 209–225.

  • Margolin, B. H., Kaplan, N., and Zeiger, E. (1981), “Statistical Analysis of the Ames Salmonella Microsome Test,” Proceedings of the National Academy of Science, 76, 3779–3783.

  • McLachlan, G. J. and Peel, D. (2000), Finite Mixture Models, John Wiley & Sons.

  • Morel, J. G. and Nagaraj, N. K. (1993), “A Finite Mixture Distribution for Modelling Multinomial Extra Variation,” Biometrika, 80, 363–371.

  • Morel, J. G. and Neerchal, N. K. (1997), “Clustered Binary Logistic Regression in Teratology Data Using a Finite Mixture Distribution,” Statistics in Medicine, 16, 2843–2853.

  • Neerchal, N. K. and Morel, J. G. (1998), “Large Cluster Results for Two Parametric Multinomial Extra Variation Models,” Journal of the American Statistical Association, 93, 1078–1087.

  • Pearson, K. (1915), “On Certain Types of Compound Frequency Distributions in Which the Components Can Be Individually Described by Binomial Series,” Biometrika, 11, 139–144.

  • Raftery, A. E. (1996), Markov Chain Monte Carlo in Practice, chapter Hypothesis Testing and Model Selection, 163–188, London: Chapman & Hall.

  • Richardson, S. (Journal of the Royal Statistical Society, Series B), “Discussion of Spiegelhalter et al.” 2002, 64, 631.

  • Roeder, K. (1990), “Density Estimation with Confidence Sets Exemplified by Superclusters and Voids in the Galaxies,” Journal of the American Statistical Association, 85, 617–624.

  • Spiegelhalter, D. J., 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, Series B, 64(4), 583–616, with discussion.

  • Titterington, D. M., Smith, A. F. M., and Makov, U. E. (1985), Statistical Analysis of Finite Mixture Distributions, New York: John Wiley & Sons.

  • Viallefont, V., Richardson, S., and Greene, P. J. (2002), “Bayesian Analysis of Poisson Mixtures,” Journal of Nonparametric Statistics, 14, 181–202.

  • Wang, P., Puterman, M. L., I., C., and Le, N. (1996), “Mixed Poisson Regression Models with Covariate Dependent Rates,” Biometrics, 52, 381–400.

  • Williams, D. A. (1975), “The Analysis of Binary Responses from Toxicological Experiments Involving Reproduction and Teratogenicity,” Biometrics, 31, 949–952.