Joint estimation of the mean and dispersion parameters in the analysis of proportions: A comparison of efficiency and bias

Canadian Journal of Statistics

Volumn 26, Issue 1, 1998, Pages 83-94

  Paul, S R ^a   Islam, A S ^a  

^a UNIVERSITY OF WINDSOR   (Canada)

Author keywords

Estimation; Extended beta binomial model; Gaussian likelihood; Mean and intraclass correlation parameters; Over underdispersion; Semiparametric procedures

Indexed keywords

EID: 0032387723     PISSN: 03195724     EISSN: None     Source Type: Journal    
DOI: 10.2307/3315675     Document Type: Article

References (28)

1. Breslow, N. (1984). Extra Poisson variation in log-linear models. Appl. Statist., 33, 38-44.
2. Breslow, N. (1990). Tests of hypotheses in over-dispersed Poisson regression and other quasi-likelihood models. J. Amer. Statist. Assoc., 85, 565-571.
3. Crowder, M.J. (1978). Beta-binomial anova for proportions. Appl. Statist. 27, 34-37.
4. Crowder, M.J. (1982). On weighted least-squares and some variants. Technical Report in Statistics, No. 13. Surrey University.
5. Crowder, M.J. (1985). Gaussian estimation for correlated binomial data. J. Roy. Statist. Soc. Ser. B, 47, 229-237.
6. Crowder, M.J. (1987). On linear and quadratic estimating functions. Biometrika, 74, 591-597.
7. Davidian, M., and Carroll, R.J. (1987). Variance function estimation. J. Amer. Statist. Assoc., 82, 1079-1091.
8. Dean, C., and Lawless, J.F. (1989). Discussion on an extension of quasi-likelihood estimation (by V.P. Godambe and M.E. Thompson). J. Statist. Plann. Inference, 22, 155-158.
9. Elston, R.C. (1977). Response to query, Consultants Corner. Biometrics, 33, 232-233.
10. Godambe, V.P., and Thompson, M.E. (1989). An extension of quasi-likelihood estimation. J. Statist. Plann. Inference, 22, 137-152.
11. Haseman, J.K., and Kupper, L.L. (1979). Analysis of dichotomous response data from certain toxicological experiments, Biometrics, 35, 281-293.
12. Inagaski, N. (1973). Asymptotic relations between the likelihood estimating function and the maximum likelihood estimator. Ann. Inst. Statist. Math., 25, 1-26.
13. Kleinman, J.C. (1973). Proportions with extraneous variance: single and independent samples. J. Amer. Statist. Assoc., 8, 46-54.
14. Liang, K.Y. (1992). Extensions of generalized linear models in the past twenty years: overview and some biomedical application. Proc. Internat. Biometric Conf.
15. Liang, K.Y., and Zeger, S.L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13-22.
16. Moore, D.F., and Tsiatis, A. (1991). Robust estimation of the standard error in moment methods for extrabinomial and extra-Poisson variation. Biometrika, 47, 383-401.
17. Nelder, J.A. (1989). Discussion on an extension of quasi-likelihood estimation (by V.P. Godambe and M.E. Thompson). J. Statist. Plann. Inference, 22, 158-160.
18. Nelder, J.A., and Lee, Y. (1992). Likelihood, quasi-likelihood and pseudo-likelihood: Some comparisons. J. Roy. Statist. Soc. Ser. B, 54, 273-284.
19. Nelder, J.A., and Pregibon, D. (1987). An extended quasi-likelihood function. Biometrika, 74, 221-232.
20. Paul, S.R. (1982). Analysis of proportions of affected foetuses in teratological experiments. Biometrics, 38, 361-370.
21. Paul, S.R., and Islam, A.S. (1995). Analysis of proportions in the presence of over/underdispersion. Biometrics, 51, 1400-1410.
22. Paul, S.R., and Islam, A.S. (1997). Joint estimation of the mean and dispersion parameters in the analysis of proportions: A comparison of efficiency and bias. Mathematics Report WMSR No. 97.02, The University of Windsor.
23. Potthoff, R.F., and Whittinghill, M. (1966). Testing for homogeneity. I. The binomial and multinomial distribution. Biometrika, 53, 167-182.
24. Prentice, R.L. (1986). Binary regression using an extended beta-binomial distribution, with discussion of correlation induced by covariate measurement errors. J. Amer. Statist. Assoc., 81, 321-327.
25. Srivastava, M.S., and Wu, Y. (1993). Local efficiency of moment estimators in beta-binomial model. Comm. Statist. Theory Methods, 22, 2471-2490.
26. Wedderburn, R.W.M. (1974). Quasi-likelihood functions, generalized linear models and the Gauss-Newton method. Biometrika, 61, 439-447.
27. Whittle, P. (1961). Gaussian estimation in stationary time series. Bull. Internat. Statist. Inst., 39, 1-26.
28. Zeger, S.L., and Liang, K.Y. (1986). Longitudinal data analysis for discrete and continuous outcomes. Biometrics, 42, 121-130.