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.

翻译：基于因子的结构方程模型依赖于以样本协方差矩阵非奇异性为前提的似然估计，但在 $p>n$ 的小样本场景下该方法失效。为此，我们提出一种新的估计原理，将协方差结构重构为自协方差与交叉协方差分量。由此建立的框架定义了一个结合相对误差约束的似然可行集，从而在 $p>n$ 的小样本场景下实现符号与方向性的稳定估计。合成数据与真实数据实验表明，该方法在恢复结构参数的符号与方向性方面具有更优的稳定性。这些结果将基于协方差的结构方程模型拓展至小样本场景，并为决策提供了具有实际应用价值的方向性信息。