Parallel Analysis (PA) is an often-recommended method for assessment of the dimensionality of a variable set. Three PA-based approaches were used to evaluate their performances in this study, they are Horn’s PA method, PA procedure based in principal axes factor analysis (PA-PAFA) method, and PA procedure based on minimum rank factor analysis (PA-MRFA) method. Sampling method for eigenvalues (normal or permutation), threshold (95% quantile or mean), and the computation for correlation matrix (Person or polychoric) were manipulated. The expectations are, first, PA-MRFA would outperform Horn’s PA and PA-PAFA in determining the number of common factors. Second, PA-PAFA yields a tendency to overfactor. Third, PA would improve performances for ordered polytomous items when the sampling distributions of eigenvalues were obtained through permutation. Finally, using polychoric correlations might increase the performance, especially in large sample sizes and conditions in which the item difficulties vary considerably across items.
The results shown that, first, the performance of PA-PAFA was inferior to those of Horn’s PA and PA-MRFA and yielded a tendency to overfactor. Second, the performaces were similar when the use of permutation as the sampling technique rather than the use of a draws from a normal distribution. Third, PA appears to be rather robust to deviations from normality and also in the context of ordered polytomous items; this finding was agree with the literatures. Fourth, polychoric-based PA procedure outperformed Pearson-based variant.
Comments & Questions
1. The ordered polytomous items were used in this study, the performance of the newly proposed method can be evaluated in other types of items.