Accuracy of Revised and Traditional Parallel Analyses for Assessing Dimensionality with Binary Data.

Area of Science:

• Psychometrics
• Statistical Modeling
• Quantitative Psychology

Background:

• Exploratory factor analysis (EFA) is crucial for understanding complex data structures.
• Parallel analysis (PA) is a common tool for determining the number of factors in EFA.
• Traditional PA (T-PA) has limitations, particularly regarding consistency with hypothesis testing.

Purpose of the Study:

• To propose and evaluate a revised parallel analysis (R-PA) method.
• To enhance the accuracy and hypothesis-testing alignment of PA in EFA.
• To compare the performance of R-PA against T-PA using Monte Carlo simulations.

Main Methods:

• Monte Carlo simulations were employed to assess method accuracy.
• Tetrachoric correlations were used for factor analysis of binary response items.
• Data generation factors included sample size, factor model type, loadings, factor correlations, and threshold distributions.

Main Results:

• R-PA demonstrated superior accuracy compared to T-PA across various conditions.
• R-PA performance improved with unidimensional models, highly correlated factors, and general/group factors.
• Higher factor loadings and larger sample sizes favored R-PA.
• T-PA frequently exhibited inflated Type I error rates.

Conclusions:

• R-PA provides a more accurate and statistically sound approach for determining the number of factors in EFA.
• The revised method is particularly beneficial for complex factor structures and binary data.
• R-PA addresses key limitations of T-PA, offering a valuable advancement for researchers.