WGR3 (MV) {bWGR}

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,npc=-1): Toy MegaLMM implementation.

09) GSEM(Y,X,npc=-1): SEM with all components for G.

10) MEGAF(Y,X,npc=-1): Float MEGA.

11) GSEMF(Y,X,npc=-1): Float GSEM.

12) XSEMF(Y,X,npc=0): GSEMF using PCs only.

In GSEM and MEGA, 'npc' means number of latent spaces if input is above zero, otherwise, 0 means all and -1 means 2*sqrt(ncol(Y)).

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

    
    # Load genomic data
    
    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))