loadings_mmes: Extract factor-analytic loadings from a fitted mmes model
In sommer: Solving Mixed Model Equations in R

loadings_mmes

R Documentation

Extract factor-analytic loadings from a fitted mmes model

Description

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`	Whether to return loadings multiplied by `sqrt(sigma2)` and specific variances multiplied by `sigma2`. When `FALSE`, both describe the dimensionless covariance shape.
`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$theta[[term]] exactly when varianceScale=FALSE, where \sigma^2 is object$covPar[[term]][1]. With varianceScale=TRUE, the returned loadings crossproduct plus the diagonal of the returned specific variances directly reproduces that covariance.

Value

A list containing:

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

Examples

## Not run: 
mix <- mmes(BLUEs ~ trial,
            random = ~ vsm(fam(trial, 2), ism(genotype)),
            rcov = ~ units, data = dt)
loadings_mmes(mix)

## End(Not run)

sommer documentation built on Oct. 24, 2026, 1:08 a.m.