Predict factor-analytic scores from a fitted mmes model

Predicts latent factor scores for each level of the main random-effect term crossed with a fam() or rrm() covariance-shaping factor, combining the fitted loadings (see loadings_mmes), the fitted covariance matrix, and the BLUPs already stored in object$uList.

Usage

scores_mmes(object, term = NULL, method = c("regression", "bartlett"), 
            varianceScale=TRUE, rotation=TRUE)

Arguments

object: a fitted model of class "mmes".
term: character name of the random term built with a single fam() or rrm() covariance-shaping factor. If NULL, the unique such term in the model is used automatically.
method: "regression" (default) uses the full fitted covariance $\Sigma$ (Thomson's method); "bartlett" uses only the specific (residual) variances $\Psi$ (Bartlett's classic unbiased estimator).
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

Let $U$ be the levels-by-levels BLUP matrix in object$uList[[term]] and $\Lambda$ the loadings from loadings_mmes. The regression (Thomson) scores are $$F = U\Sigma^{-1}\Lambda,$$ and the Bartlett scores are $$F = U\Psi^{-1}\Lambda(\Lambda^{\mathsf T}\Psi^{-1}\Lambda)^{-1}.$$ Because $U$ already contains shrunken (BLUP) effects, the resulting scores are similarly regularized.

Value

A matrix with one row per level of the main random-effect term and one column per latent factor.

Examples

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