paK {cdmTools}

Parallel analysis - dimensionality assessment method

Description

Parallel analysis with column permutation (i.e., resampling) as used in Nájera, Abad, & Sorrel (2021). It is recommended to use principal components, Pearson correlations, and mean criterion (Garrido, Abad, & Ponsoda, 2013; Nájera, Abad, & Sorrel, 2021). The parallel analysis based on principal axis factor analysis is conducted using the fa.parallel function of the psych R package (Revelle, 2020). The tetrachoric correlations are efficiently estimated using the sirt R package (Robitzsch, 2020). The graph is made with the ggplot2 package (Wickham et al., 2020).

Usage

paK(
  dat,
  R = 100,
  fa = "pc",
  cor = "both",
  cutoff = "mean",
  fm = "uls",
  plot = TRUE,
  verbose = TRUE,
  seed = NULL
)

Arguments

dat

A N individuals x J items (matrix or data.frame). Missing values need to be coded as NA.

R

Number of resampled datasets (i.e., replications) to generate. The default is 100.

fa

Extraction method to use. It includes "pc" (for principal components analysis), "fa" (for principal axis factor analysis), and "both". The default is "pc".

cor

What type of correlations to use. It includes "cor" (for Pearson correlations), "tet" (for tetrachoric/polychoric correlations), and "both". The default is "both".

cutoff

What criterion to use as the cutoff. It can be "mean" (for the average generated eigenvalues) or a value between 0 and 100 (for a percentile). A vector with several criteria can be used. The default is "mean".

fm

Factoring method to use. It includes "uls" (for unweighted least squares), "ml" (for maximum likelihood), and "wls" (for weighted least squares), among others. The default is "uls".

plot

Print the parallel analysis plot? Note that the plot might be messy if many variants are requested. The default is TRUE.

verbose

progress. The default is TRUE.

seed

A seed for obtaining consistent results. If NULL, no seed is used. The default is NULL.

Value

paK returns an object of class paK.

sug.K

The suggested number of attributes for each variant (vector).

e.values

The sample and reference eigenvalues (matrix).

plot

The parallel analysis plot. Only if plot = TRUE (plot).

specifications

Function call specifications (list).

Author(s)

Pablo Nájera, Universidad Pontificia Comillas
Miguel A. Sorrel, Universidad Autónoma de Madrid
Francisco J. Abad, Universidad Autónoma de Madrid

References

Garrido, L. E., Abad, F. J., & Ponsoda, V. (2013). A new look at Horn's parallel analysis with ordinal variables. Psychological Methods, 18, 454-474. https://doi.org/10.1037/a0030005

Nájera, P., Abad, F. J., & Sorrel, M. A. (2021). Determining the number of attributes in cognitive diagnosis modeling. Frontiers in Psychology, 12:614470. https://doi.org/10.3389/fpsyg.2021.614470

Revelle, W. (2019). psych: Procedures for Psychological, Psychometric, and Personality Research. R package version 1.9.12. https://CRAN.R-project.org/package=psych.

Robitzsch, A. (2020). sirt: Supplementary Item Response Theory Models. R package version 3.9-4. https://CRAN.R-project.org/package=sirt.

Wickham, H., et al. (2020). ggplot2: Create Elegant Data Visualisations Using the Grammar of Graphics. R package version 3.3.2. https://CRAN.R-project.org/package=ggplot2.

Examples

library(GDINA)
dat <- sim30GDINA$simdat
Q <- sim30GDINA$simQ
# In paK, R = 100 is recommended (R = 30 is here used for illustration purposes)
pa.K <- paK(dat = dat, R = 30, fa = "pc", cutoff = c("mean", 95), plot = TRUE, seed = 123)
pa.K$sug.K # Check suggested number of attributes by each parallel analysis variant
pa.K$e.values # Check eigenvalues
pa.K$plot # Show parallel analysis plot