NAM (version 1.4.2)

REML: Restricted Maximum Likelihood

Description

Univariate REML estimators and variance components for a single random variable fitted by an EMMA-like algorithm.

Usage

reml(y,X=NULL,Z=NULL,K=NULL)
MCreml(y,K,X=NULL,MC=300,samp=300)

Arguments

y

Numeric vector of observations ($n$) describing the trait to be analyzed. NA is allowed.

X

Formula or incidence matrix ($n$ by $p$) for fixed effect. NA is not allowed.

Z

Formula or numeric matrix ($n$ by $p$) that corresponds to the incidence matrix of random effect. NA is not allowed.

K

Numeric matrix ($p$ by $p$). Kinship matrix for random effect with $p$ parameters. NA is not allowed.

MC

Number of sampling procedures to estimate variance components using MCreml.

samp

Sample size of the sampling procedure to estimate variance components using MCreml.

Value

• The function reml returns a list with variance components and heritability (VC), fixed effect coefficients and standard variations (Fixed) and estimated breeding values (EBV).

Details

Solve mixed models with a single random effects minizing the log restricted maximum likelihood (REML) using the EMMA algorithm (Kang et al 2008). Prediction of random coefficients are performed according to VanRaden (2008). If y is a matrix with multiple traits, the fuctions solves the mixed model via an ECM algorithm adapted from the EMMREML package (Akdemir and Godfrey 2014). MCreml is a resampling strategy to find variance components for large datasets.

References

Akdemir, D., and O. U. Godfrey (2014) EMMREML: Fitting Mixed Models with Known Covariance Structures. R Package Version 2.0. Available at: http://CRAN.R-project.org/package=EMMREML. Kang, H. M., Zaitlen, N. A., Wade, C. M., Kirby, A., Heckerman, D., Daly, M. J., & Eskin, E. (2008). Efficient control of population structure in model organism association mapping. Genetics, 178(3), 1709-1723. VanRaden, P. M. (2008). Efficient methods to compute genomic predictions. Journal of dairy science, 91(11), 4414-4423.

Examples

# Fitting a random model
data(tpod)
FIT = reml(y=y,Z=~as.factor(fam))

# Fitting GBLUP
G = tcrossprod(gen)
G = G/mean(diag(G))
GBLUP = reml(y=y,K=G)