ABSTRACT

In the classical exploratory factor analysis (EFA) model, residuals are constrained to be uncorrelated. However, since the 1960s, extensions of the classical model that allow correlated residuals to be modeled exist. Furthermore, in many EFA applications (especially those intended for item analysis) it is highly relevant to decide whether an extended solution is more appropriate than the simpler classical solution. This decision, in turn, requires effective and powerful methods for detecting correlated residuals (doublets) when they are really present to be available. This paper discusses two existing detection approaches in the EFA context, and proposes a third, new procedure. Reference values, based on the concept of parallel analysis, are proposed for deciding the relevance of the flagged doublets in all the considered procedures. The functioning of the three procedures is assessed by using simulation, and illustrated with an illustrative example. The proposal, finally, has been implemented in a well-known noncommercial EFA program, and an implementation in R is being developed.

摘要

在经典探索性因子分析 (EFA) 模型中，残差被限制为不相关。然而，自 1960 年代以来，存在允许对相关残差进行建模的经典模型的扩展。此外，在许多 EFA 应用程序（尤其是那些用于项目分析的应用程序）中，确定扩展解决方案是否比更简单的经典解决方案更合适是高度相关的。反过来，这个决定需要有效且强大的方法来检测相关残差（双峰），当它们确实存在时可用。本文讨论了 EFA 环境中的两种现有检测方法，并提出了第三种新程序。基于平行分析的概念，提出了参考值，用于确定标记的双峰在所有考虑的程序中的相关性。通过使用模拟评估三个程序的功能，并通过说明性示例进行说明。最后，该提案已在一个著名的非商业 EFA 计划中实施，并且正在开发 R 中的实施。