Corrgrams: Exploratory displays for correlation matrices

Michael Friendly.
Corrgrams: Exploratory displays for correlation matrices.
The American Statistician, vol. 56, no. 4, pp. 316–324, 2002.

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 paper 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) re-ordering 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.

Keywords: correlation matrix; visualization, value rendering, independence, conditional independence, partial correlation, effect ordering, variable sorting, visual thinning, SAS

@Article{Friendly02corrgram,
  author = {Michael Friendly},
  year = {2002},
  journal = {The American Statistician},
  volume = {56},
  number = {4},
  pages = {316–324},
  title = {Corrgrams: Exploratory displays for correlation matrices},
  url = {http://datavis.ca/papers/corrgram.pdf},
}