Structured Factor Analysis: A Data Matrix-Based Alternative Approach to Structural Equation Modeling

Jöreskog’s covariance-based approach (JCA) has been considered a standard method for structural equation modeling. However, JCA is prone to the occurrence of improper solutions and cannot make probabilistic inferences about the true factor scores. To address the enduring issues of JCA, we propose a data matrix-based alternative, termed structured factor analysis (SFA). Given a data matrix of indicators, SFA begins by estimating both measurement model parameters and factor scores by minimizing a single cost function via an alternating least squares algorithm, which mathematically guarantees convergence to proper solutions. It then employs the factor score estimates to estimate structural model parameters. Once all parameters are estimated, SFA further estimates the probability distribution of the factor scores that can generate the data matrix of indicators, which can be used for probabilistic inferences about the true factor scores. We investigate SFA’s performance and empirical utility through simulated and real data analyses.

约雷斯科格协方差方法（Jöreskog’s covariance-based approach, JCA）长期以来被视作结构方程模型（structural equation modeling）的标准分析方法。然而，JCA易产生不恰当解，且无法针对真实因子得分开展概率推断。为解决JCA长期存在的这类固有问题，本文提出一种基于数据矩阵的替代方案，命名为结构化因子分析（structured factor analysis, SFA）。给定由观测指标构成的数据矩阵，SFA首先通过交替最小二乘算法最小化单一代价函数，同步估计测量模型参数与因子得分，该方法从数学层面保证可收敛至恰当解；随后借助因子得分的估计结果，对结构模型参数进行估计。待全部参数估计完成后，SFA进一步估计可生成该观测指标数据矩阵的因子得分概率分布，以此实现对真实因子得分的概率推断。本文通过模拟数据分析与真实数据分析，对SFA的性能与实际应用效用展开了实证探究。