Estimate factor scores for an EFA model

FACTOR_SCORES() has been superseded by efa_scores(), which is the recommended interface going forward.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 (the value psych::factor.scores() returns with Grice = TRUE); 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. 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 its estimated score. For orthogonal factors this equals the squared multiple correlation between the factor and the observed variables; for oblique factors it is the score-specific determinacy. 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))
#> ℹ `x` is not a correlation matrix; computing correlations from the raw data.
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))
#> [1] TRUE

# 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)
#> ℹ `x` is a correlation matrix; factor scores cannot be computed. Only factor
#>   weights and score diagnostics are returned. Enter raw data to get factor
#>   scores.