Genet. Sel. Evol. 39 (2007) 481-494
DOI: 10.1051/gse:20070016

Factor analysis models for structuring covariance matrices of additive genetic effects: a Bayesian implementation

Gustavo de los Campos^a and Daniel Gianola<sup>a, b, c

a</sup>  Department of Animal Sciences, University of Wisconsin-Madison, WI 53706, USA
^b  Department of Dairy Science and Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, WI 53706, USA
^c  Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, 1432 Ås, Norway

(Received 5 January 2006; accepted 28 March 2007 ; published online 27 September 2007)

Abstract - Multivariate linear models are increasingly important in quantitative genetics. In high dimensional specifications, factor analysis (FA) may provide an avenue for structuring (co)variance matrices, thus reducing the number of parameters needed for describing (co)dispersion. We describe how FA can be used to model genetic effects in the context of a multivariate linear mixed model. An orthogonal common factor structure is used to model genetic effects under Gaussian assumption, so that the marginal likelihood is multivariate normal with a structured genetic (co)variance matrix. Under standard prior assumptions, all fully conditional distributions have closed form, and samples from the joint posterior distribution can be obtained via Gibbs sampling. The model and the algorithm developed for its Bayesian implementation were used to describe five repeated records of milk yield in dairy cattle, and a one common FA model was compared with a standard multiple trait model. The Bayesian Information Criterion favored the FA model.

Key words: factor analysis / mixed model / (co)variance structures

Correspondence and reprints: gdeloscampos@wisc.edu

© INRA, EDP Sciences 2007