random.polychor.pa (version 1.1.3.2)

Parallel-Analysis-of-Polychoric-Correlations: A Parallel Analysis with Random Polychoric Correlation Matrices

Description

The function performs a parallel analysis using simulated polychoric correlation matrices. The function will extract the eigenvalues from each random generated polychoric correlation matrix and from the polychoric correlation matrix of real data. A plot comparing eigenvalues extracted from the specified real data with simulated data will help determine which of real eigenvalue outperform random data. A series of matrices comparing MAP vs PA-Polychoric vs PA-Pearson correlations methods, FA vs PCA solutions are finally presented.

Details

ll{ Package: random.polychor.pa Type: Package Version: 1.1.3.2 Date: 2011-09-02 License: GPL Version 2 or later LazyLoad: yes } The function perform a parallel analysis (Horn, 1965) using randomly simulated polychoric correlations. Generates nrep random samples of the same dimension of the empirical provided data.matrix(i.e, with the same number of participants and of variables). Items are allowed to have varying number of categories. The function will extract the eigenvalues from each randomly generated polychoric matrices and the declared quantile will be extracted. Eigenvalues from polychoric correlation matrix obtained from real data are also computed and compared, in a (scree) plot, with the eigenvalues extracted from the simulation (Polychoric matrices). Recently Cho, Li & Bandalos (2009), showed that in using PA method, it is important to match the type of the correlation matrix used to recover the eigenvalues from real data with the type of correlation matrix used to estimate random eigenvalues. Crossing the type of correlations (using Polychoric correlation matrix to estimate real eigenvalues and random simulated Pearson correlation matrice) may result in a wrong decision (i.e., retaining less non-random factors than the needed). A comparison with eigenvalues extracted from both randomly simulated Pearson correlation matrices and real data is also also included. Finally, for both type of correlation matrix (Polychoric vs Pearson), the two versions (the classic squared coefficient and the 4th power coefficient) of Velicer's MAP criterion are calculated. In version 1.1.1, a minor bug in the regarding the estimated time needed to complete the simulation is fixed. Also in this version, the function is now able to manage supplied data.matrix in which variables representing factors (i.e., variables with ordered categories) are present and may cause an error when the Pearson correlation matrix is calculated. As the poly.mat() function used to calculate the polychoric correlation matrix is going to be deprecated in favour of polychoric() function, the random.polychor.pa was consequently updated (version 1.1.2) to account for changes in psych() package. Version 1.1.3 tackles two problems signalled by users: 1) the possibility to make available the results of simulation for plotting them in other softwares. Now the random.polychor.pa will show, upon request, all the data used in the scree-plot. 2) The function polichoric() of the psych() package does not handle data matrices that include 0 as possible category and will cause the function to stop with error. So a check for the detection of the 0 code within the provided data.matrix is now added and will cause the random.polychor.pa function to stop with a warning message.

References

Cho, S.J., Li, F., & Bandalos, D., (2009). Accuracy of the Parallel Analysis Procedure With Polychoric Correlations. Educational and Psychological Measurement, 69, 748-759.

Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 32, 179-185.

O'Connor, B. P. (2000). SPSS and SAS programs for determining the number of components using parallel analysis and Velicer's MAP test. Behavior Research Methods, Instrumentation, and Computers, 32, 396-402.

Velicer, W. F. (1976). Determining the number of factors from the matrix of partial correlations. Psychometrika, 41, 321-327.

Velicer, W. F., Eaton, C. A., & Fava, J. L. (2000). Construct explication through factor or component analysis: A review and evaluation of alternative procedures for determining the number of factors or components. In R. D. Goffin & E. Helmes (Eds.), Problems and solutions in human assessment: Honoring Douglas N. Jackson at seventy (pp. 41-72). Norwell, MA: Kluwer Academic.