Factor analysis of geometric figures with four attributes: A comparison of PCA, varimax and varimin

•This study examines an analytical rotation method to complex structure (varimin).•This study compares its solutions with that of rotation to simple structure (varimax).•This study uses an experimental design with predefined components in artificial data sets.•This study finds that only a rotation to complex structure is able to identify these dimensions.

It is a common expectation that analytical rotations of factors and components aiming for a simple structure allow dimensions of intercorrelated, manifest variables to be identified with a high degree of certainty. A recently presented counter-model, the rotation to complex structure — supported by a large number of investigations — fundamentally calls this assumption into question. This paper examines the claimed advantage of a rotation to complex structure with the aid of artificially generated data structures whose components were predetermined. For similarity comparisons, it has been possible to show that only a rotation to complex structure provides interpretable and realistic solutions.