Dimensionality Assessment of Ordered Polytomous Items with Parallel Analysis
Parallel analysis (PA) is a popular approach for assessing the number of the dimensionality of a variable set. In this article, the authors discuss the key aspects to consider in selecting an optimal PA procedure that suits the properties of observed data. A series of simulations were conducted to determine which of the PA procedures would perform best as an indicator of the number of common factors of ordered polytomous items. In sum, total 18 PA procedures were implemented which were based on 12 combinations of 2 random sampling techniques, 3 extraction methods, and 2 thresholds for the Pearson-based PA; and 6 combinations of 3 extraction methods and 2 thresholds for the polychoric based PA. Results indicated that PA-MRFA performed best in indicating the correct number of major factors, followed very closely by Horn’s PA, and a distant third was PA-PAFA. The authors concluded that the Horn’s PA and PA-MRFA performed particularly well in determining the number of major factors, rather than the number of total factors. Moreover, a comparison of the polychoric- and Pearson-based procedures showed that the use of polychoric correlations yielded an improved performance, except for a slight decrease in performance for PA-MRFA with four categories.