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

• URL: http://arxiv.org/abs/2604.16894v1
• Date: Sat, 18 Apr 2026 08:03:34 GMT
• Title: Covariance-Based Structural Equation Modeling in Small-Sample Settings with $p>n$
• Abstract summary: We propose a novel estimation principle that reformulates the covariance structure into self-covariance and cross-covariance components.<n>The resulting framework defines a likelihood-based feasible set combined with a relative error constraint, enabling stable estimation in small-sample settings.<n>Experiments on synthetic and real-world data show improved stability, particularly in recovering the sign and direction of structural parameters.
• Score: 1.7205106391379026
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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