Covariance-Based Structural Equation Modeling in Small-Sample Settings with $p>n$
For researchers using SEM with high-dimensional data, this method extends applicability to small-sample settings, providing directional information for decision-making.
The paper tackles the breakdown of covariance-based SEM in small-sample settings with p>n by proposing a novel estimation principle that reformulates covariance structure into self- and cross-covariance components, enabling stable estimation of sign and direction. Experiments show improved stability in recovering structural parameters.
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.