Comparison of the K1 Rule, Parallel Analysis, and the Bass-Ackward Method on Identifying the Number of Factors in Factor Analysis

Factor analysis is widely utilized to identify latent factors underlying the observed variables. This paper presents a comprehensive comparative study of two widely used methods for determining the optimal number of factors in factor analysis, the K1 rule, and parallel analysis, along with a more recently developed method, the bass-ackward method. We provide an in-depth exploration of these techniques, discussing their historical development, advantages, and limitations. Using a series of Monte Carlo simulations, we assess the efficacy of these methods in accurately determining the appropriate number of factors. Specifically, we examine two cessation criteria within the bass-ackward framework: BA-maxLoading and BA-cutoff. Our findings offer nuanced insights into the performance of these methods under various conditions, illuminating their respective advantages and potential pitfalls. To enhance accessibility, we create an online visualization tool tailored to the factor structures generated by the bass-ackward method. This research enriches the understanding of factor analysis methodology, assists researchers in method selection, and facilitates comprehensive interpretation of latent factor structures.