Factor-analytic covariance structure

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

Usage

fam(x, k = 1L, loadings = NULL, specific = NULL, fixed = NULL)

Arguments

x

Variable defining q covariance levels.

k

Factor-analytic rank, satisfying 1 <= k < q.

loadings

Optional finite q by k starting loading matrix.

specific

Optional q positive starting specific variances.

fixed

Logical vector controlling all loading and specific-variance-ratio parameters.

Details

The factor-analytic shape is based on $$M=\Lambda\Lambda^{\mathsf T}+\Psi,$$ where \(\Psi\) is diagonal positive, followed by \(K=M/M_{11}\). For rotational identification, the leading \(k\times k\) loading block is lower triangular and its diagonal loadings are positive. The first specific variance is an internal reference; remaining specific variances are positive ratios. This removes the otherwise redundant internal scale because vsm supplies the overall \(\sigma^2\).

Value

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

See also

rrm, usm, vsm.

Examples

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