For years, dissociation studies on neurological single cases were the dominant method to infer fundamental cognitive functions in neuropsychology. In contrast, the association between deficits was considered to be of less epistemological value and even misleading. Still, principal component analysis (PCA), an associational method for dimensionality reduction, recently became popular for the identification of fundamental functions. The current study evaluated the ability of PCA to identify the fundamental variables underlying a battery of measures. Synthetic data were simulated to resemble typical neuropsychological data, including varying dissociation patterns. In most experiments, PCA succeeded to measure the underlying target variables with high up to almost perfect precision. However, this success relied on additional factor rotation. Unroated PCA struggled with the dependence of data and often failed. On the other hand, the performance of rotated factor solutions required single measures that anchored the rotation. When no test scores existed that primarily and precisely measured each underlying target variable, rotated solutions also failed their intended purpose. Further, the dimensionality of the simulated data was consistently underestimated. Commonly used strategies to estimate the number of meaningful factors appear to be inappropriate for neuropsychological data. Finally, simulations suggested a high potential of PCA to denoise data, with factor rotation providing an additional filter function. This can be invaluable in neuropsychology, where measures are often inherently noisy, and PCA can be superior to common compound measures - such as the arithmetic mean - in the measurement of variables with high reliability. In summary, PCA appears to be a powerful tool in neuropsychology that is well capable to infer fundamental cognitive functions with high precision, but the typical structure of neuropsychological data places clear limitations and a risk of a complete methodological failure on the method.
Sparse Principal Component Analysis via Fractional Function Regularity
