Enhancing Interpretability in Factor Analysis by Means of Mathematical Optimization

Area of Science:

• Statistics
• Psychometrics
• Data Analysis

Background:

• Exploratory Factor Analysis (EFA) is crucial for identifying latent structures from observed variables.
• Traditional EFA relies on rotation invariance to enhance factor interpretability via sparse loading matrices.
• Current methods may limit interpretation to the observed variables alone.

Purpose of the Study:

• To propose an optimization-based procedure for enhancing factor interpretability in EFA.
• To introduce a goodness-of-fit criterion for quantifying the quality of factor interpretation.
• To extend factor interpretation beyond observed variables using a broader set of explanatory variables.

Main Methods:

• Developed an optimization-based procedure leveraging rotation invariance for factor interpretation.
• Integrated explanatory variables, including observed variables, to assign meaning to factors.
• Introduced a novel goodness-of-fit criterion to assess the quality of factor interpretation.
• Exploited rotational invariance to find optimal orthogonal rotations matching explanatory variables.

Main Results:

• Demonstrated enhanced factor interpretability in Exploratory Factor Analysis.
• Validated the methodology on an empirical dataset (California reservoir volumes) and a synthetic dataset.
• Showcased the ability to interpret factors using a wider range of explanatory variables.

Conclusions:

• The proposed optimization-based approach significantly enhances the interpretability of factors in EFA.
• This methodology offers a more comprehensive way to understand latent variables by incorporating broader explanatory contexts.
• The approach provides a quantifiable measure of interpretation quality, advancing EFA practices.