小样本下$ p>n $时稳定估计结构方程模型的参数方向。
Covariance-Based Structural Equation Modeling in Small-Sample Settings with $p>n$
- 将协方差分解为自协方差与交叉协方差，构建可行集。
- 在$ p>n $场景中显著提升参数符号与方向的稳定性。
- 适合小样本数据、需判断变量影响方向的研究者使用。
基于因子的结构方程模型（SEM）依赖于似然估计，要求样本协方差矩阵非奇异，但在小样本且$ p>n $时失效。本文提出一种新估计原理，将协方差结构重构成自协方差和交叉协方差分量，结合相对误差约束，定义出一个基于似然的可行集，实现$ p>n $情形下对参数符号与方向的稳定估计。合成数据与真实数据实验表明，该方法在恢复参数符号与方向上表现更优，显著提升了小样本下的可靠性，扩展了基于协方差的SEM在小样本中的应用，并为决策提供可信赖的方向性信息。
原文摘要 · Abstract (English)
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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