A circumplex is a set of variables that, when plotted as vectors in N-dimensional space, fall in a circular pattern. If a set of variables forms a circumplex, the correlation matrix for the variables will have an unusual pattern called circular structure. In this pattern, the correlations on diagonal strips below the main diagonal tend to be equal, or nearly so, first becoming smaller, then larger again as you move away from the main diagonal. Below is a circular structure for an 8x8 correlation matrix.

1.00

0.80 1.00

0.60 0.80 1.00

0.40 0.60 0.80 1.00

0.20 0.40 0.60 0.80 1.00

0.40 0.20 0.40 0.60 0.80 1.00

0.60 0.40 0.20 0.40 0.60 0.80 1.00

0.80 0.60 0.40 0.20 0.40 0.60 0.80 1.00

Circumplex is a special case of a more general concept of radex, developed by Louis Guttman (who contributed a number of innovative ideas to the theory of multidimensional scaling and factor analysis, Guttman, 1954).

For an illustration, see SEPATH Example 8: Testing for Circumplex Structure.