Analysis of embryonic development with a model for under- or overdispersion relative to binomial variation

Observations from a study of the development of ovulations into embryos for Texel sheep are analysed with a model for count data that are under- or overdispersed relative to binomial variation. The analysis is based on maximum quasi-likelihood (McCullagh and Nelder, 1989, Generalized Linear Models, 2nd edition, London: Chapman and Hall), following an approach suggested by Williams (1982, Applied Statistics 31, 144-148). The dispersion parameter is developed as a combination of a variance component representing shared maternal effects and a correlation, typically negative, between ovulations within ewes. The number of ovulations (the binomial denominator) is included as an explanatory variable.