A comparison of 71 binary similarity coefficients: The effect of base rates

There are many psychological applications that require collapsing the information in a two-mode (e.g., respondents-by-attributes) binary matrix into a one-mode (e.g., attributes-by-attributes) similarity matrix. This process requires the selection of a measure of similarity between binary attributes. A vast number of binary similarity coefficients have been proposed in fields such as biology, geology, and ecology. Although previous studies have reported cluster analyses of binary similarity coefficients, there has been little exploration of how cluster memberships are affected by the base rates (percentage of ones) for the binary attributes. We conducted a simulation experiment that compared two-cluster K-median partitions of 71 binary similarity coefficients based on their pairwise correlations obtained under 15 different base-rate configurations. The results reveal that some subsets of coefficients consistently group together regardless of the base rates. However, there are other subsets of coefficients that group together for some base rates, but not for others.