LLQuadFormDiagCPP: Compute tYPY as in Zhou and Stephens eqn. 50.

In statgenQTLxT: Multi-Trait and Multi-Trial Genome Wide Association Studies

Compute tYPY as in Zhou and Stephens eqn. 50.

Description

Compute t(y) * P * y, part of the log-likelihood functions from equation 26 and 27 in Zhou and Stephens using equation 50. Equation 56, 57 and 58 are used to do the actual computations.

Usage

LLQuadFormDiagCPP(y, vInv, size_param_x = NULL)

Arguments

vInv	A n x p x p cube containing for each genotype l the p x p matrix v_l ^ {-1} (in the notation of Zhou and Stephens).
size_param_x	An optional c x n covariate matrix, c being the number of covariates and n being the number of genotypes. c has to be at least one (typically an intercept). No missing values are allowed.

Details

It is assumed that X and Y have already been rotated by Uk, where Uk is such that the kinship matrix K equals K = Uk * Dk * t(Uk).
The original X and Y are right multiplied by Uk, e.g. Y <- Y * Uk. See Zhou and Stephens (2014), supplement.
It is these rotated versions that are the input of this function.

Value

A numerical value for the t(y) * P * y part of the log-likelihood function.

References

Zhou, X. and Stephens, M. (2014). Efficient multivariate linear mixed model algorithms for genome-wide association studies. Nature Methods, February 2014, Vol. 11, p. 407–409

statgenQTLxT documentation built on May 29, 2024, 2:08 a.m.