Data sets and visualizations from Carrizosa, Guerrero, Romero Morales and Satorra (2018) \"Enhancing Interpretability in Factor Analysis by Means of Mathematical Optimization\" (article/paper under submission)

A natural approach to interpret the latent variables arising in Factor Analysis, called factors, consists of measuring explanatory variables over the same samples and assign (groups of) them to the factors. In this paper, we propose an optimization-based procedure to obtain the best assignment of the explanatory variables to a transformation of the factors, either including some information provided by the user based on his/her expertise or not. A new quality criterion to assess the interpretation to the factors given this way is also introduced. Our experimental results demonstrate the usefulness of our methodology.

对因子分析（Factor Analysis）中产生的、被称为因子（factors）的潜变量进行解释的直观方法，是在同一批样本上测量解释变量，并将（一组或多组）解释变量分配至各因子。本文提出一种基于优化的流程，可实现将解释变量最优分配至因子的变换形式，该流程可引入或不引入用户基于自身专业知识提供的先验信息。此外，本文还提出了一种全新的质量准则，用于评估此类方式得到的因子解释效果。实验结果验证了所提方法的有效性。