The major domains of psychological variation are intrinsically multivariate. Personality, cognitive ability, interests, and values can all be represented as multidimensional trait spaces and mapped at various levels of resolution—from broad-band descriptions involving a small number of abstract traits to fine-grained representations based on many narrow, specific traits. As the number of traits used to map a given domain increases, the corresponding space becomes increasingly high-dimensional, and intuitions based on low-dimensional representations become inaccurate or even misleading. The consequences for individual and group differences are profound, but have gone largely unrecognized in the psychological literature. A related issue that still awaits investigation is the impact of using alternative distance metrics, which have different psychological implications and show distinctive behaviors with increasing dimensionality. In this paper, I offer a systematic but accessible treatment of individual and group differences in multivariate domains, with a focus on high-dimensional phenomena and their theoretical implications. I begin by introducing four alternative metrics, reviewing their geometric properties, and examining the significance of those properties from a cognitive standpoint. I then discuss how these metrics behave as the number of traits increases, and their potential uses in describing individual and group variation. After considering the effects of measurement error and common methods of error correction, I conclude with an empirical example based on a large dataset of self-reported personality.

Notes on model selection with AIC (Akaike's information criterion) from my statistics courses