Recursive Estimation of Breeding Values with Categorical Data

Abstract

Recursive estimation is a process of sequential updating of parameter estimates when data become available in stages. Bayes’ theorem, which describes the accumulation of knowledge about parameters, is used to develop a recursive procedure for estimating breeding values of threshold characters. The likelihood of the data at stage k is combined with the distribution of the parameters conditional on the data after stage k−1, or prior for stage k. A second-order Taylor series approximation to the prior density is used. The mode and the matrix of second derivatives of the posterior density at stage k−1 are used to approximate the prior mean and dispersion matrix at stage k. Hence, the recursive procedure only approximates the estimates that would be obtained from analyzing all data jointly. Under normality, the results are the same. A reparameterization of the model is suggested to allow updating all parameters except for a constant specific to stage k. A numerical example is presented to illustrate the method. The proposed procedure would be useful in within-herd evaluations for calving ease, survival of the calf, liability to certain diseases, and other categorical traits of economic importance, where only data on live animals need to be stored, provided that the size of the estimation equations permits inverting the coefficient matrix.