Avoiding illusory effects in representational similarity analysis: What (not) to do with the diagonal

Representational similarity analysis (RSA) is an important part of the methodological toolkit in neuroimaging research. The focus of the approach is the construction of representational dissimilarity matrices (RDMs), which provide a single format for making comparisons between different neural data types, computational models, and behavior. We highlight two issues for the construction and comparison of RDMs. First, the diagonal values of RDMs, which should reflect within condition reliability of neural patterns, are typically not estimated in RSA. However, without such an estimate, one lacks a measure of the reliability of an RDM as a whole. Thus, when carrying out RSA, one should calculate the diagonal values of RDMs and not take them for granted. Second, although diagonal values of a correlation matrix can be used to estimate the reliability of neural patterns, these values must nonetheless be excluded when comparing RDMs. Via a simple simulation we show that inclusion of these values can generate convincing looking, but entirely illusory, correlations between independent and entirely unrelated data sets. Both of these points are further illustrated by a critical discussion of Coggan et al. (2016), who investigated the extent to which category-selectivity in the ventral temporal cortex can be accounted for by low-level image properties of visual object stimuli. We observe that their results may depend on the improper inclusion of diagonal values in their analysis.