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.
Keywords: Crawford–Ferguson family; Factorial invariance; entropy methods; orthogonal rotation; varimax.