Generalizing the use of the canonical transformation for the solution of multivariate mixed model equations

Abstract

The canonical transformation converts t correlated traits into t phenotypically and genetically independent traits. Its application to multiple trait BLUP genetic evaluations decreases computing requirements, increases the convergence rate of iterative solvers and simplifies programming. This paper presents alternative ways to retain, at least partly, these desirable characteristics in situations where the canonical transformation is theoretically impossible: when some traits are missing in some animals (including when a reduced animal model is used), when more than one random effect is included in the model and when different traits are described by different models.