WGR3 (MV) {bWGR} R Documentation

Multivariate Regression

Description

Multivariate model to find breeding values.

Usage

  mkr(Y,K)
mrr(Y,X)
mrr_float(Y,X)


Arguments

 Y Numeric matrix of observations x trait. NA is allowed. K Numeric matrix containing the relationship matrix. X Numeric matrix containing the genotyping matrix.

Details

Algorithm is described in Xavier and Habier (2022). The model for the ridge regression (mrr) is as follows:

Y = Mu + XB + E

where Y is a matrix of response variables, Mu represents the intercepts, X is the matrix of genotypic information, B is the matrix of marker effects, and E is the residual matrix.

The model for the kernel regression (mkr) is as follows:

Y = Mu + UB + E

where Y is a matrix of response variables, Mu represents the intercepts, U is the matrix of Eigenvector of K, b is a vector of regression coefficients and E is the residual matrix.

Algorithm: Residuals are assumed to be independent among traits. Regression coefficients are solved via a multivaraite adaptation of Gauss-Seidel Residual Update. Since version 2.0, the solver of mrr is based on the Randomized Gauss-Seidel algorithm. Variance and covariance components are solved with an EM-REML like approach proposed by Schaeffer called Pseudo-Expectation.

Other related implementations:

01) mkr2X(Y,K1,K2): Solves multi-trait kernel regressions with two random effects.

02) mrr2X(Y,X1,X2): Solves multi-trait ridge regressions with two random effects.

03) MRR3(Y,X,...): Extension of mrr with additional parameters.

04) MRR3F(Y,X,...): MRR3 running on float.

05) mrr_svd(Y,W): Solves mrr through the principal components of parameters.

06) MLM(Y,X,Z,maxit=500,logtol=-8,cores=1): Multivariate model with fixed effects.

07) SEM(Y,Z,PCs=3,TOI=NULL,Beta0=NULL): Fits a XFA structural equation model.

08) MEGA(Y,X): Toy MegaLMM implementation.

09) GSEM(Y,X): SEM with all components for G.

Value

Returns a list with the random effect covariances (Vb), residual variances (Ve), genetic correlations (GC), matrix with marker effects (b) or eigenvector effects (if mkr), intercepts (mu), heritabilities (h2), and a matrix with fitted values (hat).

Author(s)

Alencar Xavier, David Habier

References

Xavier, A and Habier, D. (2022). A new approach fits multivariate genomic prediction models efficiently. GSE, DOI: 10.1186/s12711-022-00730-w

Examples



data(tpod)
X = CNT(gen)

# Simulate phenotyp

sim = SimY(X)
Y = sim$Y TBV = sim$tbv

# Fit regression model

test = mrr(Y,X)

# Genetic correlation

test$GC # Heritabilies test$h2

# Accuracy

diag(cor(TBV,test\$hat))



[Package bWGR version 2.2.5 Index]