efa_scores: Estimate factor scores and score-quality diagnostics for an EFA model

Description

Computes factor-score weights (and, from raw data, the factor scores themselves) natively for an EFA() solution or a directly supplied loading matrix, together with the score-quality diagnostics that describe how well the estimated scores represent the factors: the score intercorrelations, the determinacy (validity) and univocality of each score, and Guttman's indeterminacy index. Factor scores are returned only when raw data are supplied; a correlation matrix yields the weights and diagnostics alone.

Usage

efa_scores(
  x,
  f,
  Phi = NULL,
  rho = NULL,
  method = c("regression", "Bartlett", "Anderson", "tenBerge", "Harman", "components")
)

Value

An object of class efa_scores, a list containing:

weights: The p by m factor-score weight matrix.
scores: The factor scores (n by m), or NULL when a correlation matrix was supplied.
r.scores: The m by m correlations of the factor-score estimates.
score_cor: The m by m score-factor correlation matrix; its diagonal is the determinacy (validity) of each score and its off-diagonals the univocality.
determinacy: A data frame with, per factor, the determinacy rho, the squared determinacy rho2, and Guttman's indeterminacy index guttman.
settings: A list of the settings used.

Arguments

x: data.frame or matrix. Raw data (needed to obtain factor scores) or a correlation matrix (yields weights and diagnostics only). When raw data carry column names, they are matched to the model variables by name (any extra columns are ignored, and a model variable missing from x is an error); unnamed data are matched by position.
f: object of class EFA(), a LOADINGS object, or a matrix of factor loadings.
Phi: matrix. Factor intercorrelations. Only used when a loading matrix is supplied directly in f; taken from the EFA object otherwise. Default is NULL, in which case the factors are assumed uncorrelated.
rho: matrix. Correlation matrix used to derive the scoring weights. Defaults to NULL, in which case f$orig_R is used for an EFA object and cor(x, use = "pairwise") otherwise. Pass a matrix here to score against a correlation other than the one implied by f/x.
method: character. The factor-score method: one of "regression" (default), "Bartlett", "Anderson", "tenBerge", "Harman", or "components".

Details

The p by m weight matrix W (standardized scores are scale(X) %*% W) is computed from the structure matrix S = Lambda %*% Phi, the model uniquenesses Psi = diag(1 - h2), and the scoring correlation matrix R according to method:

"regression": Thurstone's (1935) regression scores, W = R^-1 S.
"Bartlett": Bartlett's (1937) conditionally unbiased scores.
"Anderson": Anderson & Rubin's (1956) uncorrelated, unit-variance scores; defined for orthogonal factors only.
"tenBerge": ten Berge, Krijnen, Wansbeek & Shapiro's (1999) scores, which preserve the factor intercorrelations.
"Harman": Harman's (1976) idealized-variable scores.
"components": component scores, W = Lambda.

The determinacy (validity) of a score is its correlation with the factor it estimates, computed from the returned weights; for regression scores it is the multiple correlation between the factor and the observed variables (Guttman, 1955; Grice, 2001). The off-diagonal score-factor correlations give the univocality (the correlation of a score with the other factors), and 2 rho^2 - 1 is Guttman's (1955) indeterminacy index, the minimum correlation between two equally valid sets of scores. For a method other than "regression" both quantities are specific to those scores: the determinacy is the method's own score-factor correlation (never larger than the regression value), and the reported guttman follows from it.

Examples

Run this code

# Weights and score diagnostics from an EFA on a correlation matrix
efa <- EFA(test_models$baseline$cormat, n_factors = 3, N = 500,
           method = "PAF", rotation = "oblimin")
fs <- efa_scores(test_models$baseline$cormat, f = efa)
fs
summary(fs)

# Factor scores from raw data (Bartlett method)
# \donttest{
efa_raw <- EFA(GRiPS_raw, n_factors = 1, method = "PAF")
efa_scores(GRiPS_raw, f = efa_raw, method = "Bartlett")
# }

# Loadings supplied directly, with the factor intercorrelations
efa_scores(test_models$baseline$cormat, f = efa$rot_loadings, Phi = efa$Phi)