Unstructured positive-definite covariance structure

Unstructured positive-definite covariance structure. The returned dimensionless covariance shape is intended for use inside vsm, which supplies the single overall variance scale.

Usage

usm(x, theta = NULL, fixed = NULL)

Arguments

x

Variable or design defining q covariance levels.

theta

Optional positive-definite q by q starting covariance matrix.

fixed

Logical vector of length q(q+1)/2 - 1 controlling the estimable normalized-Cholesky parameters.

Details

The covariance shape is parameterized as $$K=LL^{\mathsf T},$$ with lower-triangular \(L\) and \(L_{11}=1\). Diagonal elements after the first are positive and represented on log scales; lower off-diagonal elements are unrestricted. This guarantees positive definiteness without repeatedly repairing an unconstrained covariance matrix.

Value

A list containing the incidence/design matrix in Z and a compiled CovarianceFactor v2 descriptor in covFactor, for use inside vsm.

See also

vsm, mmes.

Examples

if (FALSE) { # \dontrun{
vsm(usm(environment), ism(genotype))
} # }