Reduced-rank covariance structure

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

Usage

rrm(x, k = 1L, loadings = NULL, fixed = NULL)

Arguments

x

Variable defining q covariance levels.

k

Reduced rank, satisfying 1 <= k < q.

loadings

Optional finite q by k starting loading matrix.

fixed

Logical vector controlling the free loading parameters.

Details

The reduced-rank structure uses $$M=\Lambda\Lambda^{\mathsf T}+I_q,\qquad K=M/M_{11}.$$ The rank-\(k\) term captures the dominant covariance pattern and the identity term provides a common isotropic remainder, keeping the covariance strictly positive definite for precision-based Henderson calculations. The leading \(k\times k\) loading block is lower triangular for rotational identification, and its diagonal loadings are positive. rrm is compiled through the generic CovarianceFactor callback interface rather than requiring model-specific solver code.

Value

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

See also

fam, ownm, vsm.

Examples

if (FALSE) { # \dontrun{
vsm(rrm(environment, k=2), ism(genotype))
} # }