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.