🤖 AI Summary
This study addresses the challenge of fitting covariance-based structural equation models when the number of variables exceeds the sample size ($p > n$), a setting in which traditional factor-based approaches fail due to singularity of the sample covariance matrix. The authors propose a novel method that decomposes the covariance structure into auto-covariance and cross-covariance components, integrating a likelihood-based feasible set with relative error constraints to achieve stable estimation in small-sample regimes. This approach enables, for the first time, covariance-based structural equation modeling in $p > n$ scenarios, substantially improving parameter estimation stability and accurately recovering the signs and directions of structural parameters. Empirical evaluations on both synthetic and real-world datasets demonstrate its superior performance, highlighting its practical utility for decision-making applications.
📝 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.