# Covariance-Based Structural Equation Modeling in Small-Sample Settings with p>n

arXiv: https://arxiv.org/abs/2604.16894 · HTML: https://mlsanity.com/paper/2604.16894/

## Key facts

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- First posted on arXiv 18 Apr 2026.

## Abstract (arXiv)

Factor-based Structural Equation Modeling (SEM) relies on likelihood-based estimation assuming a nonsingular sample covariance matrix, which breaks down in small-sample settings with p>n. To address this, we propose a novel estimation principle that reformulates the covariance structure into self-covariance and cross-covariance components. The resulting framework defines a likelihood-based feasible set combined with a relative error constraint, enabling stable estimation in small-sample settings where p>n for sign and direction. Experiments on synthetic and real-world data show improved stability, particularly in recovering the sign and direction of structural parameters. These results extend covariance-based SEM to small-sample settings and provide practically useful directional information for decision-making.