An Integrated Framework for Assessing Interpretability in Exploratory Factor Analysis
Abstract
Interpretability in Exploratory Factor Analysis is characterized by the fundamental trade-off between structural sparseness and explained common variance. Lacking formal evaluation metrics, researchers frequently sacrifice parsimony in the pattern matrix to maximize the model's explanatory coverage. For this reason, we extend Hoyer's sparseness ratio into a flexible \texorpdfstring{ℒp1/ℒp2}{Lp1/Lp2} formulation to introduce the Interpretability Index I, defined as the geometric mean of explained common variance and the generalized sparseness index. We analyze the asymptotic behavior of I as norm orders increase, establishing that raising p2 alone yields a stable limit, whereas increasing p1 and p2 jointly causes the measure to saturate. The canonical choice (p1,p2)=(2,4) balances numerical stability with a smooth, tractable objective. We finally demonstrate, on five benchmark datasets from the statistical literature, how the Interpretability Index provides a systematic criterion for selecting the optimal parametrization of the latent space according to the user's analytical goals.
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BibTeX
@misc{schenone2026integrated,
title = {{An Integrated Framework for Assessing Interpretability in Exploratory Factor Analysis}},
author = {Mariaelena Bottazzi Schenone and Tiziano Iannaccio and Ilaria Mozzetta and Maurizio Vichi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33670},
eprint = {2610.33670},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33670},
}
RIS
TY - UNPB
TI - An Integrated Framework for Assessing Interpretability in Exploratory Factor Analysis
AU - Mariaelena Bottazzi Schenone
AU - Tiziano Iannaccio
AU - Ilaria Mozzetta
AU - Maurizio Vichi
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33670
UR - https://arxiv.org/abs/2610.33670
AB - Interpretability in Exploratory Factor Analysis is characterized by the fundamental trade-off between structural sparseness and explained common variance. Lacking formal evaluation metrics, researchers frequently sacrifice parsimony in the pattern matrix to maximize the model's explanatory coverage. For this reason, we extend Hoyer's sparseness ratio into a flexible \texorpdfstring{ℒ_p_1/ℒ_p_2}{Lp1/Lp2} formulation to introduce the Interpretability Index I, defined as the geometric mean of explained common variance and the generalized sparseness index. We analyze the asymptotic behavior of I as norm orders increase, establishing that raising p_2 alone yields a stable limit, whereas increasing p_1 and p_2 jointly causes the measure to saturate. The canonical choice (p_1,p_2)=(2,4) balances numerical stability with a smooth, tractable objective. We finally demonstrate, on five benchmark datasets from the statistical literature, how the Interpretability Index provides a systematic criterion for selecting the optimal parametrization of the latent space according to the user's analytical goals.
ER -