Tyler J. VanderWeele's contribution to the Discussion of ‘Vintage Factor Analysis with Varimax Performs Statistical Inference’ by Rohe & Zeng
Year: 2023
Type: article
Abstract: Rohe and Zeng (2022) have provided important results concerning properties of ‘vintage factor analysis’ that assist with interpretability, especially for non-Gaussian and leptokurtic data. I would like to focus my remarks on one particular comment, also present in Thurstone (1935) that, one aims “to ensure that each factor…. corresponds to a ‘scientifically meaningful category.’” This is an important goal, but I would argue that (i) questions of the meaning of factors always extend beyond empirical analyses; (ii) the very notion of a ‘scientifically meaningful category’ is ambiguous; and (iii) that the neglect of the prior two points has led to inappropriate interpretation of factors in practice. On the first point, the interpretation of factors is often controversial and always requires some external knowledge. Rohe and Zeng’s interpretation of their analyses, while sensible, did require the use of external features (words in journal-title; Section 3.1.1) and then still requires a reader who is aware that the cluster of title words forms a coherent whole and how to interpret that whole. Meaning is always external, and in some sense prior, to the empirical analysis (Mauran, 1996). On the second point, what is a ‘scientifically meaningful category’? The notion of a ‘discipline,’ supposedly corresponding to the factors in their analysis, is a meaningful concept, but does it correspond to a ‘scientific category’? There are various ways specific disciplines might be precisely defined, with varying levels of scope, but this then is again a conceptual, rather than an empirical, question. Moreover, the non-hierarchical nature of the categories as the number of factors increases (Section 3.1.3), indicates that while these are potentially interpretable categories, they are not fixed scientific realities. Perhaps more problematic is when factors are thought to correspond to univariate latent variables that actually represent real entities that are causally efficacious. Often it is presumed that if we had knowledge of the entity’s quantity, the indicators would be irrelevant. This assumption, however, is so strong that it has empirically testable implications even though we never observe the supposed latent variable; the assumption will often be false, and, moreover, even if such entities did exist, the factor model is still consistent with multiple causal structures (VanderWeele & Vansteelandt, 2022). Consequently, concerning the third point, the neglect of questions of meaning and different causal structures being consistent with factor models routinely results in the practice of erroneously concluding that we uncover real entities by factor analysis and that the meaning of a construct can be established by empirical analysis. Vintage factor analysis is a powerful tool for uncovering patterns of association, but we must still go through the difficult interpretative work of trying to assess why the patterns of correlation are present, and what they mean (VanderWeele, 2022; VanderWeele & Batty, 2022).
Author: Tyler J VanderWeele
Institution: Harvard University
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: hybrid
Estimated APC paid: $2,985
Awards: A Spectral Framework for Network-Driven Sampling, Scalable Statistical Inference in Small-World Networks, G4479561487, G5385673730, General Cognitive Diagnosis Models: Development, Estimation, and Applications, G6710498217, G7452299184, CAREER: Identifiability and Inferences for Structured Latent Attribute Models
OpenAlex ID: W4362677896