Highly Efficient Multivariate GREML
Abstract
Genomicrelatednessmatrix restricted maximumlikelihood (GREML) estimation of a bivariate linear mixed model (LMM) is often used for estimating the genetic correlation and covariance between traits. An extension of such... [ view full abstract ]
Genomicrelatednessmatrix restricted maximumlikelihood (GREML) estimation of a bivariate linear mixed model (LMM) is often used for estimating the genetic correlation and covariance between traits. An extension of such bivariate GREML methods is a multivariate approach. Instead of estimating multivariate LMMs, researchers often estimate pairwise bivariate LMMs for each combination of two phenotypes within a set of phenotypes. This practice for inferring genetic covariance between multiple traits can pose a problem, since the resulting (combined) covariance matrix is not necessarily positive (semi)definite. To overcome this problem, we present a multivariate GREML (MGREML) estimation method. This method consists of an iterative procedure, based on a NewtonRaphson algorithm, to obtain consistent estimates of the parameters of a multivariate SNPbased LMM for balanced data on P phenotypes, hence, observed in the same set of N individuals. We provide a parametrization of the LMM, such that resulting estimates of the P x P genetic and environment covariance matrices are positive (semi)definite, irrespective of starting values and updates of the estimates throughout the iterations. Provided one has access to the eigendecomposition of the genomicrelatedness matrix, we are able, from there on, to reduce the computational complexity of MGREML estimation from the order (NP)^{3} to an order of N(P)^{3}^{}. Therefore, the MGREML estimation method we propose can be applied to a large set of phenotypes and individuals, provided the data are balanced.
Authors

Eric A.W. Slob
(Erasmus University Rotterdam)

Ronald de Vlaming
(Vrije Universiteit Amsterdam)

Cornelius A. Rietveld
(Erasmus University Rotterdam)

Patrick J.F. Groenen
(Erasmus University Rotterdam)
Topic Area
Statistical Methods
Session
OS8A » Statistical Methods II (10:30  Saturday, 23rd June, Auditorium)
Paper
BGA_GREML_abstractV4.pdf
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