Vintage factor analysis with Varimax performs statistical inference
成果类型：
Article
署名作者：
Rohe, Karl; Zeng, Muzhe
刊物名称：
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
ISSN/ISSBN：
1369-7412
DOI：
10.1093/jrsssb/qkad029
发表日期：
2023
页码：
1037-1098
关键词：
摘要：
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.