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

TL;DR

This paper introduces a new covariance-based SEM estimation method that remains stable and accurate in small-sample scenarios where the number of variables exceeds the sample size.

Contribution

It reformulates the covariance structure into self- and cross-covariance components, enabling likelihood-based estimation in high-dimensional small-sample settings.

Findings

Improved stability in estimating structural parameters in small samples.

Accurate recovery of sign and direction of parameters.

Extension of covariance-based SEM to p>n scenarios.

Abstract

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.