Exploratory Factor Analysis with Structured Residuals for Brain Imaging Data

Dimension reduction is widely used and often necessary to reduce high dimensional data to a small number of underlying variables, making subsequent analyses and their interpretation tractable. One popular technique is Exploratory Factor Analysis (EFA), used by cognitive neuroscientists to reduce measurements from a large number of brain regions to a tractable number of factors. However, dimension reduction often ignores relevant a priori knowledge about the structure of the data. For example, it is well established that the brain is highly symmetric. In this paper, we (a) show the adverse consequences of ignoring a priori structure in factor analysis, (b) propose a technique to accommodate structure in EFA using structured residuals (EFAST), and (c) apply this technique to three large and varied brain imaging datasets, demonstrating the superior fit and interpretability of our approach. We provide an R software package to enable researchers to apply EFAST to other suitable datasets.