HSPH Biostatistics and DFCI Data Science Colloquium
Thursday April 9 at 4:00pm
HSPH, FXB 301

Tyler VanderWeele, PhD, John L. Loeb And Frances Lehman Loeb, Professor of Epidemiology, Faculty Affiliate – Department of Biostatistics, Harvard T.H. Chan School of Public Health

Factor analysis is often employed to evaluate the extent to which a single factor suffices to explain the variation in individual indicators.

However, often the resulting factors are interpreted as corresponding to a structural univariate latent variable that is itself causally efficacious. This assumption is so strong that it has empirically testable implications, even though the supposed latent variable is unobserved; statistical tests are proposed that can often reject this assumption. Factor analysis also suffers from the inability to distinguish between associations arising from causal versus conceptual relations; if two supposed factors were to causally affect one another then, over time, the process will converge to a factor model wherein only a single factor can be detected. When both positively and negatively worded items are used, factor analysis can also suggest that two factors are present even if the data were in fact generated by one. Examples of these various phenomena are given.

Despite these limitations, factor analyses can nevertheless often be informative, but requires an appropriate reinterpretation of results as reflecting a combination of causal, conceptual, and distributional relations.