The analysis of binomial data by a generalized linear mixed model

SUMMARY Methods for generalized linear models are extended to provide estimates of location and variance parameters for mixed models fitted to binomial data formed by classifying samples from an underlying normal distribution. The method estimates the parameters directly on the underlying scale. For a balanced one-way random effects model, the variance estimator simplifies to the usual analysis of variance one. The estimation of variances and the prediction of random effects for binomial traits is required by animal breeders. The predictors given are analogous to best linear unbiased predictors (Henderson, 1973) but differ from those presented by Harville & Mee (1984).

[1]  E. Dempster,et al.  Heritability of Threshold Characters. , 1950, Genetics.

[2]  J. Lush,et al.  The Heritability of Resistance to Death in the Fowl , 1948 .

[3]  C. R. Henderson.  SIRE EVALUATION AND GENETIC TRENDS , 1973 .

[4]  M. Crowder.  Inference About the Intraclass Correlation Coefficient in the Beta‐Binomial Anova for Proportions , 1979 .

[5]  H. D. Patterson,et al.  Recovery of inter-block information when block sizes are unequal , 1971 .

[6]  D. Harville.  Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems , 1977 .

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

[8]  Tom Leonard.  Bayesian methods for binomial data , 1972 .

[9]  D. Gianola,et al.  Sire evaluation for ordered categorical data with a threshold model , 1983, Génétique, sélection, évolution.

[10]  L. D. Vleck.  Estimation of Heritability of Threshold Characters , 1972 .

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

[12]  J. R. Landis,et al.  A one-way components of variance model for categorical data , 1977 .

[13]  D. Gianola.  Genetic evaluation of animals for traits with categorical responses. , 1980, Journal of animal science.

[14]  Robert W. Mee,et al.  A mixed-model procedure for analyzing ordered categorical data , 1984 .

[15]  L L Kupper,et al.  The use of a correlated binomial model for the analysis of certain toxicological experiments. , 1978, Biometrics.

[16]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[17]  Robin Thompson.  Maximum likelihood estimation of variance components , 1980 .

[18]  D. Gianola,et al.  A method of sire evaluation for dichotomies. , 1980, Journal of animal science.

[19]  N. Laird.  Empirical Bayes methods for two-way contingency tables , 1978 .