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Mixed Model, Multiple Trait Evaluation of Related Sires when all Traits are Recorded¹

University of Illinois, Urbana 61801

Abstract

The evaluation of related sires for multiple traits under mixed models is greatly simplified. When all traits are recorded for each observed individual and when fixed effect factors are the same for all traits, Kroenecker products of matrices and associated algebra can be used. The mixed model equations (modified, generalized least-squares equations) are reduced to a simple modification of the ordinary, least-squares equations. Conditions leading to evaluation of traits individually are derived. Usually computing will be facilitated by absorbing fixed effects into equations for sires. The result is a set of Tq equations for T traits and q sires. Variances and covariances associated with prediction and estimation are expressed in terms of these equations. Sire evaluations and associated variances and covariances for several linear combinations of traits, possibly based on economic values, are derived.

¹ Research supported by the Illinois Agricultural Experiment Station under project ILLU-35-346.

Present address: Animal Research Institute, Agriculture Canada, Ottawa, Ontario. K1A OC6.

Department of Dairy Science