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. |
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))