Vintage Factor Analysis with Varimax Performs Statistical Inference
Slides
Date: 04 September 2020, Friday
Time: 11am
Speaker: Dr Karl Rohe (University of Wisconsin–Madison)
Abstract:
Psychologists developed Multiple Factor Analysis to decompose multivariate data into a small number of interpretable factors without any a priori knowledge about those factors [Thurstone, 1935]. In this form of factor analysis, the Varimax "factor rotation" is a key step to make the factors interpretable [Kaiser, 1958]. Charles Spearman and many others objected to factor rotations because the factors seem to be rotationally invariant [Thurstone, 1947, Anderson and Rubin, 1956]. These objections are still reported in all contemporary multivariate statistics textbooks. This is an engima because this vintage form of factor analysis has survived and is widely popular because, empirically, the factor rotation often makes the factors easier to interpret. In a recent paper, we overturned a great deal of this controversy. We showed that Principal Components Analysis (PCA) with the Varimax rotation provides a unified spectral estimation strategy for a broad class of modern factor models (https://arxiv.org/abs/2004.05387).
This talk has three parts (kind of like Psychotherapy!). Part I will return to the origin of the factor analysis misunderstanding. Part II will clarify what was misunderstood. Part III will create a new and unified understanding. This new understanding has clear implications for practice. With a sparse eigensolver, PCA with Varimax is both fast and stable. Combined with Thurstone’s straightforward diagnostics, this vintage approach is suitable for a wide array of modern applications. For example, in my applied work on social networks, PCA with Varimax easily scales (on my laptop) to graphs with millions of nodes.
Zoom Link: https://uni-sydney.zoom.us/j/91302353477
Meeting ID: 91302353477
Slides