cpgen (version 0.1)

cGBLUP: Genomic BLUP

Description

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 $\mathbf{G}$

Usage

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)

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

burnin

Burnin

seed

Seed

verbose

Prints progress to the screen

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

Details

Kang et al. (2008): $$\mathbf{y} = \mathbf{Xb} + \mathbf{a} + \mathbf{e} \textrm{ with: } \mathbf{a} \sim MVN(\mathbf{0},\mathbf{G}\sigma^2_a)$$

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: $$Var(\mathbf{U'y}) = \mathbf{U'G'U} \sigma^2_a + \mathbf{U'U} \sigma^2_e$$ $$\mathbf{U'UDU'U}\sigma^2_a + \mathbf{I}\sigma^2_e$$ $$\mathbf{D}\sigma^2_a + \mathbf{I}\sigma^2_e$$

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.

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.

See Also

clmm, cgrm, cGWAS.emmax

Examples

# generate random data
rand_data(500,5000)

# compute a genomic relationship-matrix
G <- cgrm(M,lambda=0.01)

# run model
mod <- cGBLUP(y,G)