Discussion: “Vintage Factor Analysis with Varimax Performs Statistical Inference” by Rohe and Zeng
Discussion: “Vintage Factor Analysis with Varimax Performs Statistical Inference” by Rohe and Zeng
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讨论：Rohe 和 Zeng 的“使用 Varimax 进行统计推断的老式因子分析”
DOI：
10.1093/jrsssb/qkad040
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Xu, Gongjun
中科院分区：
文献类型：
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作者：
Chen, Yunxiao;Xu, Gongjun
在20世纪30年代，心理学家开始开发多因素分析，将多变量数据分解为少量可解释的因素，而无需任何关于这些因素的先验知识。在这种形式的因子分析中，方差最大因子旋转通过多维因子重绘轴，使其稀疏，从而使其更易于解释。查尔斯斯皮尔曼和其他许多人反对因子旋转，因为因子似乎是旋转不变的。尽管存在争议，但因子轮换在分析数据的人中仍然广泛流行。扭转近世纪的统计思想的主题，我们表明，旋转使因素更容易解释，因为方差最大值进行统计推断，特别是，主成分分析（PCA）与方差最大值旋转提供了一个统一的谱估计策略，广泛的一类半参数因子模型，包括随机块模型和自然变化的潜在狄利克雷分配。此外，我们表明，瑟斯顿的广泛采用的稀疏诊断隐含评估一个关键的尖峰条件，使这些模型中的轴统计可识别。PCA与Varimax是快速，稳定，实用。结合Thurstone的直接诊断，这种老式的方法适用于各种现代应用。
In the 1930s, Psychologists began developing Multiple-Factor Analysis to decompose multivariate data into a small number of interpretable factors without any a priori knowledge about those factors. In this form of factor analysis, the Varimax factor rotation redraws the axes through the multi-dimensional factors to make them sparse and thus make them more interpretable. Charles Spearman and many others objected to factor rotations because the factors seem to be rotationally invariant. Despite the controversy, factor rotations have remained widely popular among people analyzing data. Reversing nearly a century of statistical thinking on the topic, we show that the rotation makes the factors easier to interpret because the Varimax performs statistical inference; in particular, principal components analysis (PCA) with a Varimax rotation provides a unified spectral estimation strategy for a broad class of semi-parametric factor models, including the Stochastic Blockmodel and a natural variation of Latent Dirichlet Allocation. In addition, we show that Thurstone’s widely employed sparsity diagnostics implicitly assess a key leptokurtic condition that makes the axes statistically identifiable in these models. PCA with Varimax is fast, stable, and practical. Combined with Thurstone’s straightforward diagnostics, this vintage approach is suitable for a wide array of modern applications.