FACTOR_SCORES: Estimate factor scores for an EFA model

In EFAtools: Fast and Flexible Implementations of Exploratory Factor Analysis Tools

Estimate factor scores for an EFA model

Description

FACTOR_SCORES() has been superseded by efa_scores(), which is the recommended interface going forward. It remains available so existing code keeps working. Note that R2 is now the squared factor-score determinacy of the requested method: the squared correlation between a factor and the scores that method produces. For method = "Thurstone" this is each factor's squared multiple correlation with the observed variables (the value psych::factor.scores() returns with Grice = TRUE); for every other method it is smaller, because no estimator correlates more highly with the factor than the regression estimator does. Earlier versions returned psych's default Grice = FALSE validity coefficient, so the slot is not comparable across versions.

A convenience wrapper around efa_scores() that returns factor scores and weights in a compact list. Factor scores are calculated according to the specified method if raw data are provided, and only factor weights if a correlation matrix is provided.

Usage

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

Arguments

x	data.frame or matrix. Dataframe or matrix of raw data (needed to get factor scores) or matrix with correlations.
f	object of class efa_fit() or matrix.
Phi	matrix. A matrix of factor intercorrelations. Only needs to be specified if a factor loadings matrix is entered directly into f; for an efa_fit() object the intercorrelations are taken from the object, and a supplied Phi is ignored with a warning. Default is NULL, in which case the intercorrelations of a directly supplied loading matrix are assumed to be zero.
rho	matrix. Correlation matrix used to derive the scoring weights. Defaults to NULL, in which case the matrix the EFA in f was fit on (f$orig_R) is used, so the weights stay consistent with the loadings even for a non-Pearson correlation (e.g. polychoric); for a directly supplied loading matrix, x itself is used when it is a correlation matrix, otherwise the Pearson correlation of x. Pass a matrix here to score against a different correlation.
method	character. The method used to calculate factor scores. One of "Thurstone" (regression-based; default), "tenBerge", "Anderson", "Bartlett", "Harman", or "components".

Value

A list of class FACTOR_SCORES containing the following:

scores	The factor scores (only if raw data are provided.)
weights	The factor weights.
r.scores	The correlations of the factor score estimates.
missing	Whether the raw data contained missing values (only if raw data are provided).
R2	The squared factor-score determinacy for each factor: the squared correlation between a factor and the score the requested method produces. For method = "Thurstone" this equals the squared multiple correlation between the factor and the observed variables; for every other method it is specific to those scores and smaller. See efa_scores() for the underlying score-quality diagnostics.
settings	A list of the settings used.

See Also

efa_scores() for the factor-score weights together with the full set of score-quality diagnostics (determinacy, univocality, and Guttman indeterminacy index) and a print/summary method.

Examples

# Example with raw data with method "Bartlett"
EFA_raw <- efa_fit(DOSPERT_raw, n_factors = 10, estimator = "PAF",
                   rotation = "oblimin",
                   rotate_control = rotate_control(random_starts = 1))
fac_scores_raw <- FACTOR_SCORES(DOSPERT_raw, f = EFA_raw, method = "Bartlett")

# Same as above, but with raw data AND a correlation matrix
cor_pearson <- cor(DOSPERT_raw)
EFA_cor_pearson <- efa_fit(cor_pearson, n_factors = 10, N = nrow(DOSPERT_raw),
                           estimator = "PAF", rotation = "oblimin",
                           rotate_control = rotate_control(random_starts = 1))
fac_scores_cor_pearson <- FACTOR_SCORES(DOSPERT_raw, f = EFA_cor_pearson,
                                        rho = cor_pearson,
                                        method = "Bartlett")

# Scores between two alternatives above are identical
isTRUE(all.equal(fac_scores_raw$scores, fac_scores_cor_pearson$scores,
                 check.attributes = FALSE))

# Example with a correlation matrix only (does not return factor scores)
EFA_cor <- efa_fit(test_models$baseline$cormat, n_factors = 3, N = 500,
                   estimator = "PAF", rotation = "oblimin")
fac_scores_cor <- FACTOR_SCORES(test_models$baseline$cormat, f = EFA_cor)

EFAtools documentation built on Aug. 21, 2026, 5:16 p.m.