Parameter Estimation of the Beta-Binomial Distribution: An Application Using the Sas Software
DOI:
https://doi.org/10.5902/2179460X17512Keywords:
beta-binomial distribution, regression model, data analysisAbstract
In this paper we describe the parameter estimation of the beta-binomial distribution using the procedure NLMIXED of the SAS software. The beta-binomial distribution is a discrete mixture distribution which can capture overdispersion in the data. The estimation of parameters of the beta-binomial distribution can lead to computational problems, since it does not belong to the exponential family and there are not explicit solutions for the maximum likelihood estimation. Using a real dataset, we show that the SAS software can be satisfactorily used for the estimation of the parameters. We also consider the possibility of including a covariate in the model. The SAS codes used in this paper are given in an Appendix.
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Aeschbacher, H. U., Vuataz, L., Sotek, J., Stalder, R. (1977). Use of the beta-binomial distribution in dominant-lethal testing for “weak mutagenic activity” Part 1. Mutation Research/Fundamental and Molecular Mechanisms of Mutagenesis, 44(3), 369–390.
Burnham, K. P., Anderson, D. R. (2003). Model selection and inference: a practical information-theoretic approach. Springer-Verlag, New York.
Chatfield, C., Goodhardt, G. J. (1976). The beta-binomial model for consumer purchasing behaviour. In: Mathematical Models in Marketing, pp. 53–57. Springer Berlin Heidelberg.
Crowder, M. J. (1978). Beta-binomial ANOVA for proportions. Journal of the Royal Statistical Society. Series C (Applied Statistics), 27(1), 34–37.
Gange, S. J., Munoz, A., Saez, M., Alonso, J. (1996). Use of the beta-binomial distribution to model the effect of policy changes on appropriateness of hospital stays. Journal of the Royal Statistical Society. Series C (Applied Statistics), 45(3), 371–382.
Griffiths, D. A. (1973). Maximum likelihood estimation for the beta-binomial distribution and an application to the house-hold distribution of the total number of cases of a disease. Biometrics, 29(4), 637–648.
Haseman, J. K., Kupper, L. L. (1979). Analysis of dichotomous response data from certain toxicological experiments, Biometrics, 35(1), 281–293.
Kleinman, J. C. (1978). Proportions with extraneous variance: single and independent samples. Journal of the American Statistical Association, 68(341), 46–53.
Koenig, H. G., Büssing, A. (2010). The Duke University Religion Index (DUREL): a five-item measure for use in epidemological studies. Religions, 1(1), 78–85.
Littell, R. C., Milliken, G. A., Stroup, W. W., Wolfinger, R. D., Schabenberger, O. (2006). SAS for Mixed Models. Second Edition. Cary: SAS Institute.
Martinez, E. Z., Santos-Almeida, R. G., Carvalho, A. C. D. (2012). Propriedades da Escala de Religiosidade de Duke em uma amostra de pós-graduandos. Revista de Psiquiatria Clínica, 39:(5), 180.
Morgan, B. J. T. (1992). Analysis of quantal response data. London: Chapman and Hall.
Pearson, E. S. (1925). Bayes’ theorem, examined in the light of experimental sampling. Biometrika, 17(3/4), 388–442.
Skellam, J. G. (1948). A probability distribution derived from the binomial distribution by regarding the probability of success as variable between the sets of trials. Journal of the Royal Statistical Society. Series B, 10(2),
–261.
Smith, D. M. (1983). Maximum likelihood estimation of the parameters of the beta binomial distribution. Journal of the Royal Statistical Society. Series C (Applied Statistics), 32(2), 196–204.
Tamura, R. N., Young, S. S. (1987). A stabilized moment estimator for the beta-binomial distribution. Biometrics, 43, 813–824.
Yamamoto, E., Yanagimoto, T. (1992). Moment estimators for the beta-binomial distribution. Journal of Applied Statistics, 19(2), 273–283.
Williams, D. A. (1975). The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity. Biometrics, 31(4), 949–952.
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