MLM REML {NAM} | R Documentation

## 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.

### 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 for ridge-type model are performed according to VanRaden (2008), and kernel-type model via RKHS according to de los Campos et al. (2010).

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 based on subsampling with `samp` observations at a time, repeating the procedure `MC` times. Subsampling is a common Monte Carlo strategy to reduce the computational burden to estimate variance components in large datasets.

### 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).

### Author(s)

Alencar Xavier, Tiago Pimenta and Shizhong Xu

### 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.

de los Campos, G., Gianola, D., Rosa, G. J., Weigel, K. A., & Crossa, J. (2010). Semi-parametric genomic-enabled prediction of genetic values using reproducing kernel Hilbert spaces methods. Genetics Research, 92(04), 295-308.

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

    ## Not run:
    # Fitting a random model
    data(tpod)
    FIT = reml(y=y,Z=~as.factor(fam))

    # Fitting GBLUP
    G = GRM(gen)
    GBLUP = reml(y=y,K=G)

    # GBLUP vs RRBLUP
    g = tcrossprod(gen)
    gblup = reml(y=y,K=g)
    rrblup = reml(y=y,Z=gen)
    rbind(gblup$VC,rrblup$VC)
    gebv_gblup = gblup$EBV
    gebv_rrblup = c(tcrossprod(t(rrblup$EBV),gen))
    plot(gebv_gblup,gebv_rrblup)

    ## End(Not run)

[Package NAM version 1.7.2 Index]