Relative density clouds: Visualizing and exploring multivariate patterns of group differences

Abstract

This paper introduces relative density clouds, a simple but powerful method to visualize the relative density of two groups in multivariate space. Relative density clouds employ k-nearest neighbor density estimates to provide information about group differences throughout the entire distribution of the variables. The method can also be used to decompose overall group differences into the specific contributions of differences in location, scale, and covariation. Existing relative distribution methods offer a flexible toolkit for the analysis of univariate differences; relative density clouds bring some of the same advantages to fruition in the context of multivariate research. They can assist in the exploration of complex patterns of group differences, and help break them down into simpler, more interpretable effects. An easy-to-use R function is provided to make this visualization method widely accessible to researchers.