Enhancing Interpretability in Factor Analysis by Means of Mathematical Optimization

Emilio Carrizosa, Vanesa Guerrero*, Dolores Romero Morales, Albert Satorra

*Corresponding author for this work

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Exploratory Factor Analysis (EFA) is a widely used statistical technique to discover the structure of latent unobserved variables, called factors, from a set of observed variables. EFA exploits the property of rotation invariance of the factor model to enhance factors’ interpretability by building a sparse loading matrix. In this paper, we propose an optimization-based procedure to give meaning to the factors arising in EFA by means of an additional set of variables, called explanatory variables, which may include in particular the set of observed variables. A goodness-of-fit criterion is introduced which quantifies the quality of the interpretation given this way. Our methodology also exploits the rotational invariance of EFA to obtain the best orthogonal rotation of the factors, in terms of the goodness-of-fit, but making them match to some of the explanatory variables, thus going beyond traditional rotation methods. Therefore, our approach allows the analyst to interpret the factors not only in terms of the observed variables, but in terms of a broader set of variables. Our experimental results demonstrate how our approach enhances interpretability in EFA, first in an empirical dataset, concerning volumes of reservoirs in California, and second in a synthetic data example.
Original languageEnglish
JournalMultivariate Behavioral Research
Issue number5
Pages (from-to)748-762
Number of pages15
Publication statusPublished - Sept 2020

Bibliographical note

Published online: 30. October 2019
The research presented in the contribution was funded by the H2020 Marie Skłodowska-Curie Actions grant ‘Research and Innovation Staff Exchange Network of European Data Scientists' (#822214 – NeEDS).


  • Exploratory factor analysis
  • Interpretability
  • Factor rotation
  • Explanatory variables
  • Mathematical optimization

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