Pairwise Target Rotation for Factor Models

Abstract

Factor analysis is used to characterize latent variables by examining relationships among manifest variables. In exploratory factor analysis (EFA), various factor models are considered to uncover the latent structure. Now, the success of EFA lies with the model's interpretability, as the objective is to build a factor model that is not only supported by data, but is also meaningful. Achieving such, however, is challenging, as gauging interpretability is difficult and subjective, owing to rotational indeterminacy. Thus, we propose a new index that measures the interpretability of a factor model. The index does this by evaluating the agreement between a priori information, such as semantic information from items, and the loadings. We also introduce pairwise target rotation, a rotation method that maximizes interpretability based on the index. In general, this method allows for an intuitive yet flexible way of incorporating a priori information, such as semantics, in factor rotations, which can help in performing EFA more effectively. Based on simulations, the index correctly indicates better fit when noise levels are lower and the new rotation outperforms classical orthogonal rotations across diverse conditions in terms of recovering the latent structure. Finally, we applied the method to empirical datasets, providing evidence linking item semantics and latent constructs, consistent with recent findings.