Instituto de Matemáticas de la Universidad de Sevilla (IMUS), Seville, Spain.
Department of Statistics, Universidad Carlos III de Madrid, Getafe, Spain.
Multivariate Behav Res. 2020 Sep-Oct;55(5):748-762. doi: 10.1080/00273171.2019.1677208. Epub 2019 Oct 30.
Exploratory Factor Analysis (EFA) is a widely used statistical technique to discover the structure of latent unobserved variables, called factors, from a set of observed variables. EFA exploits the property of rotation invariance of the factor model to enhance factors' interpretability by building a sparse loading matrix. In this paper, we propose an optimization-based procedure to give meaning to the factors arising in EFA by means of an additional set of variables, called , which may include in particular the set of observed variables. A goodness-of-fit criterion is introduced which quantifies the quality of the interpretation given this way. Our methodology also exploits the rotational invariance of EFA to obtain the best orthogonal rotation of the factors, in terms of the goodness-of-fit, but making them match to some of the explanatory variables, thus going beyond traditional rotation methods. Therefore, our approach allows the analyst to interpret the factors not only in terms of the observed variables, but in terms of a broader set of variables. Our experimental results demonstrate how our approach enhances interpretability in EFA, first in an empirical dataset, concerning volumes of reservoirs in California, and second in a synthetic data example.
探索性因子分析（EFA）是一种广泛使用的统计技术，用于从一组观测变量中发现潜在的未观测变量（称为因子）的结构。EFA 利用因子模型的旋转不变性特性，通过构建稀疏加载矩阵来增强因子的可解释性。在本文中，我们提出了一种基于优化的方法，通过一组额外的变量（称为 ）赋予 EFA 中出现的因子以意义，这组变量可能特别包括观测变量集。引入了一个拟合优度准则，用于量化这种解释的质量。我们的方法还利用 EFA 的旋转不变性来获得最佳的因子正交旋转，以拟合优度为目标，但使它们与一些解释变量相匹配，从而超越传统的旋转方法。因此，我们的方法允许分析师不仅根据观测变量，而且根据更广泛的变量集来解释因子。我们的实验结果表明，我们的方法如何在 EFA 中增强可解释性，首先在一个关于加利福尼亚水库体积的经验数据集上，其次在一个合成数据示例上。
