A generalized Lp1 /Lp2 approach to measure the interpretability of latent variable models

Interpretability in latent variable modeling is defined by a fundamental trade-off between structural sparseness and explained vari-ance. However, in practice, parsimony of the loading structure is fre-quently sacrificed to maximize fit, due to a lack of formal evaluation metrics. To address this, we propose a synthetic measure that explicitly integrates explanatory power and structural simplicity. By extending an established metric of sparseness basedon the L_1/L_2 norm ratio into a flexible L_p1/L_p2 formulation, we define interpretability as the geomet-ric mean of explained variance and component-wise sparseness. Through simulations and an application to economic growth data, we show how the metric facilitates model selection within two f rameworks: standard dimensionality reduction (PCA vs. Disjoint PCA) and simultaneous unit-clustering (Reduced K-Means vs. Clustering Disjoint PCA).