Pairwise Target Rotation for Factor Models

2024-09-17

AI Summary

Factor interpretability in Exploratory Factor Analysis (EFA) lacks quantifiable criteria and effective guidance mechanisms. Method: We propose PrioriMax, a novel differentiable pairwise target rotation framework that supports the seamless incorporation of arbitrary prior knowledge—such as semantic constraints—thereby overcoming the rigidity of conventional orthogonal or oblique rotations in interpretability control. PrioriMax jointly optimizes matrix rotation and differentiable factor loading reconstruction to maximize a newly defined interpretability objective. An open-source Python package, *interpretablefa*, enables plug-and-play deployment. Results: Evaluated on the Experiences in Close Relationships (ECR) scale, PrioriMax significantly improves semantic consistency of extracted factors and boosts researchers’ interpretation accuracy by 23.6%. Our core contribution is the establishment of a computable, intervenable, and generalizable paradigm for factor interpretability in EFA.

Technology Category

• Machine Learning: Transparent, Interpretable, Explainable ML
• Knowledge Representation and Reasoning: Preferences
• Computer Vision: Interpretability, Explainability, and Transparency

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Enhancing interpretability in exploratory factor analysis models
• Incorporating prior information flexibly into factor rotations
• Providing a Python tool for intuitive factor analysis

Innovation

• Pairwise target rotation for factor interpretability
• Incorporates prior information in factor rotations
• Python implementation with interpretablefa package