Psychology Department, University of Notre Dame, 390 Corbett Family Hall, Notre Dame, IN, 46556, USA.
Soka University, Tokyo, Japan.
Psychometrika. 2023 Sep;88(3):865-887. doi: 10.1007/s11336-022-09877-3. Epub 2022 Jul 22.
Applications of structural equation modeling (SEM) may encounter issues like inadmissible parameter estimates, nonconvergence, or unsatisfactory model fit. We propose a new factor rotation method that reparameterizes the factor correlation matrix in exploratory factor analysis (EFA) such that factors can be either exogenous or endogenous. The proposed method is an oblique rotation method for EFA, but it allows directional structural paths among factors. We thus referred it to as FSP (factor structural paths) rotation. In particular, we can use FSP rotation to "translate" an SEM model to incorporate theoretical expectations on both factor loadings and structural parameters. We illustrate FSP rotation with an empirical example and explore its statistical properties with simulated data. The results include that (1) EFA with FSP rotation tends to fit data better and encounters fewer Heywood cases than SEM does when there are cross-loadings and many small nonzero loadings, (2) FSP rotated parameter estimates are satisfactory for small models, and (3) FSP rotated parameter estimates are more satisfactory for large models when the structural parameter matrices are sparse.
结构方程模型（SEM）的应用可能会遇到不可接受的参数估计、不收敛或模型拟合不理想等问题。我们提出了一种新的因子旋转方法，该方法对探索性因子分析（EFA）中的因子相关矩阵进行了重新参数化，使得因子可以是外生的或内生的。所提出的方法是 EFA 的一种斜交旋转方法，但它允许因子之间存在有向结构路径。因此，我们称之为 FSP（因子结构路径）旋转。特别是，我们可以使用 FSP 旋转将 SEM 模型“转换”为包含因子载荷和结构参数理论预期的模型。我们通过一个实证示例说明了 FSP 旋转，并使用模拟数据探讨了其统计性质。结果包括：（1）当存在交叉载荷和许多小非零载荷时，FSP 旋转的 EFA 往往比 SEM 更能拟合数据，并且遇到的 Heywood 情况更少；（2）对于小模型，FSP 旋转的参数估计令人满意；（3）当结构参数矩阵稀疏时，对于大模型，FSP 旋转的参数估计更为令人满意。
