Dimension reduction is widely used and often necessary to reduce high dimensional data to a small number of underlying variables -factors or componentsto make data analyses and their interpretation tractable. One popular technique is Exploratory Factor Analysis (EFA), which extracts factors when the underlying factor structure is not known. However, we observe that datasets exist where researchers indeed do not know the factor structure, but do have other relevant a priori knowledge. For instance, cognitive neuroscientists may want to reduce individual differences in brain structure across a large number of regions to a tractable number of factors. In this field, it is well established that the brain displays contralateral symmetry, such that the same regions in the left and right half of the brain will be highly correlated. Here, a) we show the adverse consequences of ignoring such a priori structure in standard factor analysis, b) we propose a technique for Exploratory factor analysis with structured residuals (EFAST) which accommodates such a priori structure into an otherwise standard EFA, and c) we apply this technique to a large (N = 647, 68 brain regions) empirical dataset, demonstrating the superior fit and improved intepretability of our approach. We provide an R software package to allow researchers to apply this technique to other suitable datasets.
Contents1 Introduction 2 2 Factor analysis with structured residuals 43 Simulations 9 4 EFAST in practice: Modeling brain morphology 14 5 Summary and discussion 22 6 Acknowledgements 23Appendices 27 1 extract factors when these factors are measured in different ways: when measuring personality through a self-report questionnare and behaviour ratings, there are factors that explain correlation among items corresponding to a specific trait such as 'extraversion', and there are factors that explain additional correlation between items because they are gathered using the same methods (self-report and behavioural ratings). Thus, MTMM techniques separate the correlation matrix into two distinct, summative parts: correlation due to the traits of central interest, and correlation due to the measurement methods. However, MTMM requires a priori knowledge of the trait structure (e.g., the OCEAN model of personality).Here we propose a manner in which to instead conduct purely exploratory factor analysis (e.g. across many brain regions), whilst incorporating prior structure knowledge (e.g. symmetry). Standard implementations of EFA, CFA, and MTMM are inadequate to estimate factor structure under these circumstances, as they do not simultaneously allow for exploration and the incorporation of residual structure. We improve upon these procedures by developing a method called Exploratory factor analysis with structured residuals (EFAST). We show that EFAST outperforms EFA in empirically plausible scenarios, and that ignoring the problem of structured residuals in these scenarios adversely affects inferences.Note that we are not the first to suggest using structured residua...