Principal Component and Factor Analytic Models In International Sire Evaluation

Abstract

Various studies have addressed the challenge of variance component estimation for multiple-trait across country evaluation (MACE) and attempted to ease the burden of the estimation process. Several of these have focused on using the decomposition of the genetic covariance matrices into the pertaining matrices of eigenvalues and -vectors, namely principal component (PC) and factor analytic (FA) approaches (e.g., Leclerc et al., 2005; Mäntysaari, 2004). For highly correlated traits, some eigenvalues have only a very small effect on the genetic variation. This is utilized by ignoring the PCs with negligible effects. For the PC approach this results in dimension reduction. The FA model also includes trait specific variances. This results in a full rank (co)variance (VCV) matrix unless some of the latter are zero. Leclerc et al. (2005) studied both PC and FA approaches for a sub-set of well-linked base countries, performing dimension reduction for this sub-set and estimating the contribution of the remaining countries to these PCs or factors. Mäntysaari (2004) introduced a bottom-up PC approach: this begins with a sub-set of countries, adding in the remaining countries sequentially. By examining in each step whether or not the new country increases the rank of the genetic VCV matrix, it only fits PCs with non-negligible eigenvalues and thus avoids over-parameterized models. Direct estimation of the important genetic principal components only has been proposed by Kirkpatrick and Meyer (2004). However, this requires the appropriate rank to be known or to be estimated. Similarly, we can estimate a VCV matrix imposing a FA structure directly. The bottom-up approach has recently been tested for variance component estimation for MACE with promising results (Tyrisevä et al., 2009). Both direct PC and FA approaches have been applied to beef cattle data sets, and have demonstrated their potential to be used for large, multi-trait data sets (e.g., Meyer, 2007a). The objectives of this study are to assess the impact of alternative parameterizations (PC and FA) for the estimation of variance components on practical predictions of breeding values with MACE.