Modelling the Extraneous Variance in the Presence of Extra‐Binomial Variation

Two widely used methods for fitting proportions exhibiting extra‐binomial variation are maximum likelihood under a beta‐binomial model and a moment method based on the structure of the mean and variance. Both of these methods are extended to allow modelling the extra‐binomial component of the variance as a function of the mean. The methods are illustrated using a set of chromosome aberration data.

[1]  Martin Crowder,et al.  Beta-binomial Anova for Proportions , 1978 .

[2]  N. Breslow.  Extra‐Poisson Variation in Log‐Linear Models , 1984 .

[3]  Wayne A. Fuller,et al.  Least Squares Estimation When the Covariance Matrix and Parameter Vector are Functionally Related , 1980 .

[4]  R. Prentice,et al.  The analysis of chromosomally aberrant cells based on beta-binomial distribution. , 1984, Radiation Research.

[5]  Ross L. Prentice,et al.  Likelihood inference in a correlated probit regression model , 1984 .

[6]  Dirk F. Moore,et al.  Asymptotic properties of moment estimators for overdispersed counts and proportions , 1986 .

[7]  Ross L. Prentice,et al.  Binary Regression Using an Extended Beta-Binomial Distribution, with Discussion of Correlation Induced by Covariate Measurement Errors , 1986 .

[8]  T. Sofuni,et al.  Relationship between the radiation dose and chromosome aberrations in atomic bomb survivors of Hiroshima and Nagasaki. , 1978, Journal of radiation research.

[9]  Leonard A. Stefanski,et al.  The effects of measurement error on parameter estimation , 1985 .

[10]  David R. Cox.  The analysis of binary data , 1970 .

[11]  R. W. Wedderburn.  Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method , 1974 .

[12]  R. Brooks,et al.  Approximate Likelihood Ratio Tests in the Analysis of Beta‐Binomial Data , 1984 .

[13]  Haseman Jk,et al.  Analysis of dichotomous response data from certain toxicological experiments. , 1979 .

[14]  Stephen E. Fienberg,et al.  Discrete Multivariate Analysis: Theory and Practice , 1976 .

[15]  D. A. Williams,et al.  Extra‐Binomial Variation in Logistic Linear Models , 1982 .

[16]  Joel C. Kleinman,et al.  Proportions with Extraneous Variance: Single and Independent Samples , 1973 .

[17]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[18]  Williams Da,et al.  The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity. , 1975 .