Scree Test Optimal Coordinate (STOC)

The STOC (Raiche et al., 2013) approach is based on fitting \(I-2\) (\(I\) is the number of observed variables) two point regression models using the (i+1)th and I-th (the last one) eigenvalue to obtain a prediction for the i-th eigenvalue that is referred to as optimal coordinate (with p being the number of observed variables and therefore also the number of eigenvalues). If the observed empirical eigenvalue is larger than the predicted optimal coordinate. Raiche et al. (2013) also argue for a restricted version that retains only factors with an eigenvalue greater than the reference eigenvalue by PA (holds PCA and quant=0.95 in this package).

STOC(
  response,
  fa = "pc",
  nfact = 1,
  cor.type = "pearson",
  use = "pairwise.complete.obs",
  vis = TRUE,
  plot = TRUE
)

Arguments

response

A required N × I matrix or data.frame consisting of the responses of N individuals to I items.

fa

A string that determines the method used to obtain eigenvalues in PA. If "pc", it represents Principal Component Analysis (PCA); if "fa", it represents Principal Axis Factoring (a widely used Factor Analysis method; @seealso factor.analysis; Auerswald & Moshagen, 2019). (Default = "pc")

nfact

A numeric value that specifies the number of factors to extract, only effective when fa = 'fa'. (Default = 1)

cor.type

A character string indicating which correlation coefficient (or covariance) is to be computed. One of "pearson" (default), "kendall", or "spearman". @seealso cor.

use

an optional character string giving a method for computing covariances in the presence of missing values. This must be one of the strings "everything", "all.obs", "complete.obs", "na.or.complete", or "pairwise.complete.obs" (default). @seealso cor.

vis

A Boolean variable that will print the factor retention results when set to TRUE, and will not print when set to FALSE. (default = TRUE)

plot

A Boolean variable that will print the STOC plot when set to TRUE, and will not print it when set to FALSE. @seealso plot.STOC. (Default = TRUE)

Value

An object of class STOC, which is a list containing the following components:

nfact

The number of factors to retain by both Optimal Coordinate and PA.

nfact.STOC

The number of factors to retain only by Optimal Coordinate.

nfact.PA

The number of factors to retain only by PA.

fa

Indicates the method used to obtain eigenvalues. 'pc' represents Principal Component Analysis, and 'fa' represents Principal Axis Factoring.

eigen.value

A vector containing the empirical eigenvalues.

eigen.ref

A vector containing the reference eigenvalues by both Optimal Coordinate and PA.

References

Raiche, G., Walls, T. A., Magis, D., Riopel, M., & Blais, J.-G. (2013). Non-graphical solutions for Cattell's scree test. Methodology, 9(1), 23-29. https://doi.org/10.1027/1614-2241/a000051

Goretzko, D. (2025). How many factors to retain in exploratory factor analysis? A critical overview of factor retention methods. Psychological methods, Advance online publication. https://doi.org/10.1037/met0000733

See also

STOC

Examples

library(EFAfactors)
set.seed(123)

##Take the data.bfi dataset as an example.
data(data.bfi)

response <- as.matrix(data.bfi[, 1:25]) ## loading data
response <- na.omit(response) ## Remove samples with NA/missing values

## Transform the scores of reverse-scored items to normal scoring
response[, c(1, 9, 10, 11, 12, 22, 25)] <- 6 - response[, c(1, 9, 10, 11, 12, 22, 25)] + 1

# \donttest{
 STOC.obj <- STOC(response, plot=FALSE)
#> The number of factors suggested by STOC is 5 .

 ## STOC plot
 plot(STOC.obj)


# }