# cGBLUP: Genomic BLUP In cgenpp: Parallel genomic evaluations

## Description

This function allows fitting a mixed model with one random effect besides the residual. The random effect \mathbf{a} follows some covariance-structure \mathbf{G}

## Usage

 1 2 cGBLUP(y,G,X=NULL, scale_a = 0, df_a = -2, scale_e = 0, df_e = -2, niter = 10000, burnin = 5000, seed = NULL, verbose=FALSE) 

## Arguments

 y vector of phenotypes G Relationship matrix / covariance structure for random effects X Optional Design Matrix for fixed effects. If omitted a column-vector of ones will be assigned scale_a prior scale parameter for a df_a prior degrees of freedom for a scale_e prior scale parameter for e df_e prior degrees of freedom for e niter Number of iterations used by clmm burnin Burnin for clmm seed Seed for clmm verbose Prints progress to the screen

## Details

Kang et al. (2008):

\mathbf{y} = \mathbf{Xb} + \mathbf{a} + \mathbf{e} \textrm{ with: } \mathbf{a} \sim MVN(\mathbf{0},\mathbf{G}σ^2_a)

By finding the decomposition: \mathbf{G = UDU'} and premultiplying the model equation by \mathbf{U'} we get:

\mathbf{U'y = U'Xb + U'a + U'e}

with:

Var(\mathbf{U'y}) = \mathbf{U'G'U} σ^2_a + \mathbf{U'U} σ^2_e

\mathbf{U'UDU'U}σ^2_a + \mathbf{I}σ^2_e

\mathbf{D}σ^2_a + \mathbf{I}σ^2_e

After diagonalization of the variance-covariance structure the transformed model is being fitted by passing \mathbf{D}^{1/2} as the design matrix for the random effects to clmm. The results are subsequently backtransformed and returned by the function.

## Value

List of 6:

 var_e Posterior mean of the residual variance var_a Posterior mean of the random-effect variance b Posterior means of the fixed effects a Posterior means of the random effects posterior_var_e Posterior of the residual variance posterior_var_u Posterior of the random variance

Claas Heuer

## References

Kang, H. M., N. A. Zaitlen, C. M. Wade, A. Kirby, D. Heckerman, M. J. Daly, and E. Eskin. "Efficient Control of Population Structure in Model Organism Association Mapping." Genetics 178, no. 3 (February 1, 2008): 1709-23. doi:10.1534/genetics.107.080101.

clmm, clmm.CV, cGWAS.emmax
  1 2 3 4 5 6 7 8 9 10 11 ## Not run: # generate random data rand_data(500,5000) # compute a genomic relationship-matrix G <- cgrm(M,lambda=0.01) # run model mod <- cGBLUP(y,G) ## End(Not run)