Learn R Programming

statgenQTLxT (version 1.0.3)

LLQuadFormDiagCPP: 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)

Value

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

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.

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