Department of Experimental Psychology, Heinrich Heine University Düsseldorf, Universitätsstr. 1, 40225, Düsseldorf, Germany.
Behav Res Methods. 2024 Oct;56(7):7241-7260. doi: 10.3758/s13428-024-02417-0. Epub 2024 May 6.
An essential step in exploratory factor analysis is to determine the optimal number of factors. The Next Eigenvalue Sufficiency Test (NEST; Achim, 2017) is a recent proposal to determine the number of factors based on significance tests of the statistical contributions of candidate factors indicated by eigenvalues of sample correlation matrices. Previous simulation studies have shown NEST to recover the optimal number of factors in simulated datasets with high accuracy. However, these studies have focused on continuous variables. The present work addresses the performance of NEST for ordinal data. It has been debated whether factor models - and thus also the optimal number of factors - for ordinal variables should be computed for Pearson correlation matrices, which are known to underestimate correlations for ordinal datasets, or for polychoric correlation matrices, which are known to be instable. The central research question is to what extent the problems associated with Pearson correlations and polychoric correlations deteriorate NEST for ordinal datasets. Implementations of NEST tailored to ordinal datasets by utilizing polychoric correlations are proposed. In a simulation, the proposed implementations were compared to the original implementation of NEST which computes Pearson correlations even for ordinal datasets. The simulation shows that substituting polychoric correlations for Pearson correlations improves the accuracy of NEST for binary variables and large sample sizes (N = 500). However, the simulation also shows that the original implementation using Pearson correlations was the most accurate implementation for Likert-type variables with four response categories when item difficulties were homogeneous.
探索性因素分析的一个重要步骤是确定最佳因素数量。最近提出的下一个特征值充分性检验（NEST；Achim，2017）是一种基于样本相关矩阵特征值的候选因素的统计贡献的显著性检验来确定因素数量的方法。以前的模拟研究表明，NEST 在模拟数据集上能够非常准确地恢复最佳因素数量。然而，这些研究主要集中在连续变量上。本研究探讨了 NEST 在有序数据上的性能。对于有序变量的因素模型（因此也包括最佳因素数量）是否应该基于 Pearson 相关矩阵进行计算，这一直存在争议，因为 Pearson 相关矩阵已知会低估有序数据集的相关性，或者基于 polychoric 相关矩阵进行计算，因为 polychoric 相关矩阵已知是不稳定的。核心研究问题是，与 Pearson 相关和 polychoric 相关相关的问题会在何种程度上恶化 NEST 对有序数据集的应用。提出了针对有序数据集的 NEST 实现方法，利用 polychoric 相关。在一项模拟研究中，将针对有序数据集的提议实现方法与原始的 NEST 实现方法进行了比较，原始的 NEST 实现方法即使对于有序数据集也计算 Pearson 相关。模拟结果表明，用 polychoric 相关替代 Pearson 相关可以提高 NEST 对二值变量和大样本量（N=500）的准确性。然而，模拟结果也表明，对于具有四个反应类别且项目难度均匀的 Likert 型变量，使用 Pearson 相关的原始实现方法是最准确的实现方法。
