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Comparison data

Source: R/efa_cd.R
efa_cd.Rd

Factor retention method introduced by Ruscio and Roche (2012). The code was adapted from the CD code by Auerswald and Moshagen (2019) available at https://osf.io/x5cz2/?view_only=d03efba1fd0f4c849a87db82e6705668

Usage

efa_cd(
  x,
  n_factors_max = NA,
  N_pop = 10000,
  N_samples = 500,
  alpha = 0.3,
  cor_method = c("pearson", "spearman", "kendall", "poly", "tetra"),
  max_iter = 50
)

Source

Auerswald, M., & Moshagen, M. (2019). How to determine the number of factors to retain in exploratory factor analysis: A comparison of extraction methods under realistic conditions. Psychological Methods, 24(4), 468–491. https://doi.org/10.1037/met0000200

Ruscio, J., & Roche, B. (2012). Determining the number of factors to retain in an exploratory factor analysis using comparison data of known factorial structure. Psychological Assessment, 24, 282–292. doi: 10.1037/a0025697

Arguments

x

data.frame or matrix. Dataframe or matrix of raw data.

n_factors_max

numeric. The maximum number of factors to test against. Larger numbers will increase the duration the procedure takes, but test more possible solutions. If left NA (default) the maximum number of factors for which the model is still over-identified (df > 0) is used.

N_pop

numeric. Size of finite populations of comparison data. Default is 10000.

N_samples

numeric. Number of samples drawn from each population. Default is 500.

alpha

numeric. The alpha level used to test the significance of the improvement added by an additional factor. Default is .30.

cor_method

character. One of "pearson", "spearman", or "kendall", passed to stats::cor(). "poly" and "tetra" are not supported because CD compares the data against simulated continuous reference data. Default is "pearson".

max_iter

numeric. The maximum number of iterations after which the iterative PAF procedure inside the comparison-data generation is halted; it does not cap an EFA of x. Default is 50.

Value

An object of class efa_retention (see print.efa_retention() and plot.efa_retention() for the print and plot methods). Its main fields are:

n_factors

A named numeric vector ("CD") with the suggested number of factors according to comparison data results.

results

A list with a single record holding the mean RMSE between the eigenvalues of the generated and the entered data per number of factors (used for the plot) and, in rmse_eigenvalues, the per-sample RMSE matrix (rows are samples, columns are factor counts; columns beyond the last tested factor count are left as zero).

settings

A list of the settings used.

Details

Comparison data (CD) extends parallel analysis by reproducing the observed correlation matrix rather than generating random data: datasets with a known factor structure are generated with an increasing number of factors, and the smallest number for which adding a further factor no longer significantly improves the reproduction of the observed eigenvalues is retained (Ruscio & Roche, 2012).

Note that if the data contains missing values, these will be removed for the comparison data procedure using stats::na.omit(). If missing data should be treated differently, e.g., by imputation, do this outside efa_cd() and then pass the complete data.

See also

efa_retain() as a wrapper function for this and the other factor retention criteria.

Other factor retention criteria: efa_ekc(), efa_hull(), efa_kgc(), efa_map(), efa_nest(), efa_parallel(), efa_retain(), efa_scree(), efa_smt()

Examples

# \donttest{
# determine n factors of the GRiPS
efa_cd(GRiPS_raw)
#> ── Comparison data ─────────────────────────────────────────────────────────────
#> 
#> • Suggested number of factors: 1

# determine n factors of the DOSPERT risk subscale
efa_cd(DOSPERT_raw)
#> ── Comparison data ─────────────────────────────────────────────────────────────
#> 
#> • Suggested number of factors: 9
# }