In the social sciences, measurement scales often consist of ordinal items and are commonly analyzed using factor analysis. Either data are treated as continuous, or a discretization framework is imposed in order to take the ordinal scale properly into account. Correlational analysis is central in both approaches, and we review recent theory on correlations obtained from ordinal data. To ensure appropriate estimation, the item distributions prior to discretization should be (approximately) known, or the thresholds should be known to be equally spaced. We refer to such knowledge as substantive because it may not be extracted from the data, but must be rooted in expert knowledge about the data-generating process. An illustrative case is presented where absence of substantive knowledge of the item distributions inevitably leads the analyst to conclude that a truly two-dimensional case is perfectly one-dimensional. Additional studies probe the extent to which violation of the standard assumption of underlying normality leads to bias in correlations and factor models. As a remedy, we propose an adjusted polychoric estimator for ordinal factor analysis that takes substantive knowledge into account. Also, we demonstrate how to use the adjusted estimator in sensitivity analysis when the continuous item distributions are known only approximately.

中文翻译：

---

对序数项进行因子分析需要对响应边际有深入的了解。


在社会科学中，测量量表通常由序数项组成，并且通常使用因子分析进行分析。要么将数据视为连续数据，要么采用离散化框架以正确考虑序数尺度。相关分析是这两种方法的核心，我们回顾了从序数数据获得的相关性的最新理论。为了确保适当的估计，离散化之前的项目分布应该是（大约）已知的，或者阈值应该是等距的。我们将此类知识称为实质性知识，因为它可能不是从数据中提取的，但必须植根于有关数据生成过程的专家知识。给出了一个说明性案例，其中缺乏项目分布的实质性知识不可避免地导致分析人员得出结论：真正的二维案例完全是一维的。其他研究探讨了违反基本正态性的标准假设会在多大程度上导致相关性和因子模型的偏差。作为一种补救措施，我们提出了一种用于序数因子分析的调整后的多向估计量，该估计量考虑了实质性知识。此外，我们还演示了当连续项分布仅近似已知时如何在敏感性分析中使用调整估计量。