The analysis of binomial data by a generalized linear mixed model

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).