cGBLUP: Genomic BLUP
In cpgen: Parallelized Genomic Prediction and GWAS

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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=TRUE)

`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
`burnin`	Burnin
`seed`	Seed
`verbose`	Prints progress to the screen

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.

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

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, cgrm, cGWAS.emmax

## 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)