Pairwise Target Rotation for Factor Models

Abstract: Factor analysis is a way to characterize the relationships between many manifest variables in terms of a smaller number of latent variables (i.e., factors). Particularly, in exploratory factor analysis (EFA), researchers consider various factor models by exploiting rotational indeterminacy to uncover underlying structures and identify factors. Generally, the success of EFA lies with the factor models' interpretabilities, which can be difficult to achieve or measure. To help address this problem, a new interpretability criterion is constructed, as well as a rotation method based on it that is called pairwise target rotation or priorimax. Pairwise target rotation allows for an intuitive yet flexible way of incorporating arbitrary prior information, such as semantics, in factor rotations, which can help the researcher perform EFA more effectively. The implementation of the proposed method is written in Python 3 and is made available together with several helper functions through the package interpretablefa on the Python Package Index. A demonstration of the method is provided using data on Experiences in Close Relationships Scale obtained from the Open-Source Psychometrics Project.