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.
Highlights
Multivariate mixed models are used in quantitative genetics to describe, for example, several traits measured on an individual [6,7,8], or a longitudinal series of measurements of a trait, e.g., [23], or observations on the same trait in different environments [19]
Posterior means of the log-likelihoods were −19 706.57 and −19 696.85 for the factor analysis (FA) and multiple trait (MT) models, respectively, indicating that both models had similar “fit”
Posterior means and posterior standard deviations were similar for both models, and this is expected because the FA model imposes no restriction on the mean vector
Summary
Multivariate mixed models are used in quantitative genetics to describe, for example, several traits measured on an individual [6,7,8], or a longitudinal series of measurements of a trait, e.g., [23], or observations on the same trait in different environments [19]. While none of the genetic correlations may be equal to one, the vector of additive genetic values may be approximated reasonably well by a linear combination of a smaller number of random variables, or common factors Another approach to multiple-trait analysis is to redefine the original records, so as to reduce dimension. E.g., [3], consists of reducing the number of traits first, followed by fitting a quantitative genetic model to some common factors or principal components. A quantitative genetic model is fitted to the transformed data Another approach fits a multiple trait model in the first step [1, 11], leading to an estimate of the genetic (co)variance matrix, with each measure treated as a different trait. A discussion of possible extensions of the model is given in the concluding section
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
