Package 'fspe'

Estimating number of factors with out-of-sample prediction error

Description

Estimates the number of factors in Exploratory Factor Analysis (EFA) by approximating the out-of-sample prediction errors using a cross-validation scheme.

Usage

fspe(data, maxK, nfold = 10, rep = 1, method = "PE",
     rotate = "oblimin", pbar = TRUE, ...)

Arguments

data	A n x p matrix or data.frame.
maxK	The largest number of factors considered. For example, if maxK = 8, the factors 1, 2, ..., 8 are considered.
nfold	The number of folds in the cross-validation scheme. Defaults to nfold = 10.
rep	The number of repetitions of the cross-validation scheme. The repetiations are aggregated by averaging the prediction errors for each number of factor and subsequently selecting the number of factors that minimizes this average. Defaults to rep = 1.
method	If method = "PE", the factor estimation is based on the prediction error on the variables; If method = "Cov" the error is computed on the covariance matrix. Defaults to method = "PE" since it has performed better in simulations (see Haslbeck & van Bork, 2021 below.)
rotate	The totation being used in the underlying factor analysis models. The options are the same as in the fa() function in the psych package, which is called by fpse. Defaults to rotate = "oblimin".
pbar	If pbar = TRUE, a progress bar is shown.
...	Additional arguments passed to the fa() function in the psych package.

Details

The function returns:

Value

nfactor	An integer indicating the estimated number of factors.
nfactor	A 4-dimensional (for the PE method: variables, candidate models, folds, repetitions) or a 3-dimensional (for the Cov method: candidate models, folds, repetitions) array containing all prediction errors.

Author(s)

Jonas Haslbeck <[email protected]>

References

Haslbeck & van Bork (2021). Estimating the number of factors in Exploratory Factor Analysis using out-of-sample prediction errors. PsyArXiv Preprint: https://psyarxiv.com/qktsd

Examples

data(holzinger19)

fspe_out <- fspe(holzinger19,
                 maxK = 10,
                 nfold = 10,
                 method = "PE")

fspe_out$nfactor # estimated factors = 4

# Plot OoS PE path
plot(fspe_out$PEs, xlab="No. Factors", ylab="OoS PE")

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Psychometric example data set by Holzinger & Swineford (1936)

Description

19 ability measurements from the classic psychometrics data set of Holzinger and Swineford (1939). The original data set contains 24 variables, however, we excluded the last four to obtain an example data set for four factors (see Harman, 1967). We took this dataset from the R-package psychTools (Revelle & Revelle, 2020).

Usage

data(holzinger19)

References

Harman, Harry Horace (1967), Modern factor analysis. Chicago, University of Chicago Press.

Holzinger, K. J., & Swineford, F. (1939). A study in factor analysis: The stability of a bi-factor solution. Supplementary Educational Monographs, no. 48. Chicago: University of Chicago, Department of Education.

Revelle, W. (2020). Package ‘psychTools’.

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