A Computationally Simple Bayesian Method for Estimation of Heterogeneous Within-Herd Phenotypic Variances

¹ Department of Dairy Science, University of Wisconsin, Madison 53706

Heterogeneous variance among subclasses of the data (e.g., herds) is a potential source of bias in livestock genetic evaluation. The BLUP method can account for such heterogeneity if variance components within each subclass are known; unfortunately, information within a particular subclass is generally insufficient to estimate variances or variance components accurately. Procedures based on empirical Bayes methods and structural models for variance components have been derived but are not yet computationally feasible on a large scale. Therefore, computationally simpler approximations based on phenotypic variances have been proposed and utilized, but these lack, so far, theoretical support. In this study, a Bayesian procedure for combining within- and across-subclass phenotypic variances is presented, and a numerical example is given. This method offers the computational simplicity of other approximate procedures based on phenotypic variances, but it also possesses a stronger theoretical justification. In a simulation study involving an average of approximately 1.6 million observations in 44,000 region-herd-year-parity subclasses, the Bayesian method compared favorably with other currently available methods for combining within- and across-subclass phenotypic variances.

Key Words: heterogenous variance • Bayesian methods

Submitted on May 21, 1992
Accepted on July 31, 1992

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