Extract factor-analytic loadings from a fitted mmes model

Reconstructs the normalized loadings matrix and specific variances of a fam() or rrm() covariance-shaping factor fitted inside vsm(), on the same scale as the fitted covariance matrix returned in object$theta.

Usage

loadings_mmes(object, term = NULL, varianceScale=TRUE, rotation=TRUE)

Arguments

object: a fitted model of class "mmes".
term: character name of the random term (matching a name in object$covStruct) built with a single fam() or rrm() covariance-shaping factor. If NULL, the unique such term in the model is used automatically; an error is raised if none or more than one exist.
varianceScale: a logical argument to indicate if loadings should be returned in variance scale (multiplied by sqrt(sigma2)).
rotation: a logical value to indicate if loadings should be rotated by its singular vectors.

Details

fam()/rrm() remove their otherwise redundant internal scale so that vsm() owns the single overall variance; the loadings and specific variances reported by loadings_mmes are re-normalized so that $$\Sigma = \sigma^2(\Lambda\Lambda^{\mathsf T}+\Psi)$$ reproduces object$theta[[term]] exactly, where $\sigma^2$ is object$covPar[[term]][1].

Value

A list containing:

loadings: a levels-by-factor matrix $\Lambda$.
specific: a named vector of specific variances $\Psi$ (identically 1 for every level in a rrm() term).
sigma2: the fitted overall variance scale.
model: "fa" or "rr".
term: the resolved term name.

Examples

if (FALSE) { # \dontrun{
mix <- mmes(BLUEs ~ trial,
            random = ~ vsm(fam(trial, 2), ism(genotype)),
            rcov = ~ units, data = dt)
loadings_mmes(mix)
} # }