Corrgrams

TLDR

Correlation and covariance matrices underpin classical multivariate methods, yet few exploratory visual displays exist for moderately large variable sets. The article introduces “corrgram,” a set of techniques for visualizing correlation matrices. Corrgrams render correlation magnitudes and signs, reorder variables to cluster similar ones, and extend to conditional and partial independence matrices, with a SAS implementation. The authors demonstrate that corrgrams can be applied to conditional and partial independence matrices and provide accessible SAS code for use.

Abstract

Correlation and covariance matrices provide the basis for all classical multivariate techniques. Many statistical tools exist for analyzing their structure but, surprisingly, there are few techniques for exploratory visual display, and for depicting the patterns of relations among variables in such matrices directly, particularly when the number of variables is moderately large. This article describes a set of techniques we subsume under the name “corrgram,” based on two main schemes: (a) Rendering the value of a correlation to depict its sign and magnitude. We consider some of the properties of several iconic representations, in relation to the kind of task to be performed. (b) Reordering the variables in a correlation matrix so that "similar" variables are positioned adjacently, facilitating perception. In addition, the extension of this visualization to matrices for conditional independence and partial independence is described and illustrated, and we provide an easily used SAS implementation of these methods.