Department of psychology, University of Torino, Torino, Italy.
Department of Human and Social Sciences, University of Aosta Valley, Aosta, Italy.
Multivariate Behav Res. 2021 Sep-Oct;56(5):787-804. doi: 10.1080/00273171.2020.1770571. Epub 2020 Jun 16.
A large number of methods of factor rotation are available in the literature, but the development of formal criteria by which to compare them is an understudied field of research. One possible criterion is the Thurstonian concept of "factorial invariance", which was applied by Kaiser to the varimax rotation method in 1958 and has been subsequently neglected. In the present study, we propose two conditions for establishing whether a method satisfies factorial invariance, and we apply them to 11 orthogonal rotation methods. The results show that 3 methods do not exhibit factorial invariance under either condition, 3 are invariant under one but not the other, and 5 are invariant under both. Varimax rotation is one of the 5 methods that satisfy factorial invariance under both conditions and is the only method that satisfies the invariance condition originally advocated by Kaiser in 1958. From this perspective, it appears that varimax rotation is the method that best ensures factorial invariance.
有大量的因子旋转方法在文献中可用，但开发正式的标准来比较它们是一个研究不足的领域。一个可能的标准是 Thurstonian 的“因子不变性”概念，Kaiser 于 1958 年将其应用于方差极大旋转法，此后就被忽视了。在本研究中，我们提出了两种确定方法是否满足因子不变性的条件，并将其应用于 11 种正交旋转方法。结果表明，有 3 种方法在这两种条件下都不具有因子不变性，有 3 种方法在一种条件下具有不变性，但在另一种条件下不具有不变性，有 5 种方法在两种条件下都具有不变性。方差极大旋转法是满足两种条件下因子不变性的 5 种方法之一，也是唯一一种满足 Kaiser 于 1958 年最初提出的不变性条件的方法。从这个角度来看，方差极大旋转法似乎是最能保证因子不变性的方法。
