Beta‐Binomial Distribution - Rosner - 2005 - Major Reference Works - Wiley Online Library

The beta-binomial distribution results from a beta distribution mixture of binomials. It is useful for clustered binary data, for which the ordinary binomial distribution is usually inappropriate because different observations are correlated rather than independent. Models using this distribution permit the mean to depend on explanatory variables. An implicit assumption of the distribution is that subunits are exchangeable within a cluster. Generalizations of it allow for data structures with multiple levels of nesting.

References

1 Connolly, M. A. & Liang, K. Y. (1988). Conditional logistic regression models for correlated binary data, Biometrika 75, 501–506.
10.1093/biomet/75.3.501
Web of Science® Google Scholar
2 Crowder, M. J. (1978). Beta-binomial ANOVA for proportions, Applied Statistics 27, 34–37.
10.2307/2346223
Google Scholar
3 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.
10.2307/2529131
CAS PubMed Web of Science® Google Scholar
4 Prentice, R. L. (1986). Binary regression using an extended beta-binomial distribution, with discussion of correlation induced by covariate measurement errors, Journal of the American Statistical Association 394, 321–327.
Web of Science® Google Scholar
5 Qu, Y. S., Williams, G. W., Beck, G. J. & Goormastic, M. (1987). A generalized model of logistic regression for correlated data, Communications in Statistics 16, 3447–3476.
10.1080/03610928708829585
Web of Science® Google Scholar
6 Rosner, B. (1984). Multivariate methods in ophthalmology with application to other paired data situations, Biometrics 40, 1025–1035.
10.2307/2531153
CAS PubMed Web of Science® Google Scholar
7 Rosner, B. (1989). Multivariate methods for clustered binary data with more than one level of nesting, Journal of the American Statistical Association 84, 373–380.
Web of Science® Google Scholar
8 Rosner, B. (1992). Multivariate methods for binary longitudinal data with heterogeneous correlation over time, Statistics in Medicine 11, 1915–1928.
10.1002/sim.4780111412
CAS PubMed Web of Science® Google Scholar
9 Rosner, B. (1992). Multivariate methods for clustered binary data with multiple subclasses, with application to binary longitudinal data, Biometrics 48, 721–731.
10.2307/2532339
CAS PubMed Web of Science® Google Scholar
10 Smith, D. M. (1983). Maximum likelihood estimation of the parameters of the beta-binomial distribution (algorithm AS189), Applied Statistics 32, 196–204.
10.2307/2347299
PubMed Google Scholar
11 Williams, D. A. (1975). The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity, Biometrics 31, 949–952.
10.2307/2529820
CAS PubMed Web of Science® Google Scholar

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