Decoding 3 Categories of Conventional Wisdom in Pattern Similarity Analyses

Abstract

Many methods in neuroscience characterize shared patterns of activity through the analysis of covariance matrices. Depending on the experimental designs and dimensions of interest, the domains of these analyses are sometimes referred to as functional connectivity, pattern similarity analysis, or inter-subject correlation. Progress in these domains has led to a richer understanding of the brain. However, unexpected properties of commonly employed covariance methods within these domains calls into question conventional wisdom that sometimes motivates analyses. While the common practice of averaging pairwise correlations within- and across-groups of observations may appear straightforward, and comparing these within- and across-group averages is simple to perform, researchers often rely on verbal explanations of what such a contrast might mean.

In this dissertation, we show that these verbal explanations rest on stringent assumptions, and as such, do not hold without qualification. Procedures which selectively average groups prior to correlating, or use elaborate forms of parceling the data and correlating across parcels, rely on the same—often implicit—assumptions. Throughout this paper we demonstrate that these analyses can be viewed as special cases of a latent factor model, in which all of the variances of the latent factors are assumed to be equal. Moreover, this model is not only able to explain such procedures, but has been studied and extended across the social, health, and physical sciences. As a result, we draw connections to analogous issues discussed in the behavioral psychology and psychometric literatures. The first section of this dissertation is empirical research on individual differences in working memory and intelligence, that uses a latent factor model common to individual differences psychology. The second section of this dissertation uses this model to evaluate the three aforementioned procedures in neuroscience.

Such a perspective is valuable because it creates a clear mapping between methodological issues that were (and often continue to be) widespread in covariance analyses from behavioral psychology and their neuroscience counterparts.