A1401
Title: Assessing and comparing rotation methods using Thurstone's simple structure criteria
Authors: Kohei Uno - Nagasaki University (Japan) [presenting]
Tomoyuki Nakagawa - Meisei University (Japan)
Takayuki Kawashima - Institute of Science Tokyo (Japan)
Abstract: Factor rotation is an important step in exploratory factor analysis because it transforms estimated factor loading matrices into interpretable structures. Many rotation methods have been developed to achieve simple structure and are theoretically motivated by Thurstone's simple structure criteria. However, they typically do not directly optimize Thurstone's original conditions, because these conditions are not formulated as convenient objective functions for numerical optimization. Instead, existing methods rely on alternative rotation criteria that are computationally tractable while aiming at simple structure. Five conditions corresponding closely to Thurstone's criteria are formalized as quantitative indices for a rotated loading matrix. These indices cover sparsity within factors, sparsity within variables, factor complexity, variable complexity, and separation of substantial loadings. Using the proposed indices, a broad set of orthogonal and oblique rotation methods is compared mainly through numerical simulation studies, with empirical data examples used to illustrate practical implications. The simulations vary the number of factors, sample size, loading pattern, factor correlation, and noise level to evaluate when each rotation method approximates Thurstone's criteria.
