, Volume 57, Issue 4, pp 469–497

Circumplex models for correlation matrices

  • Michael W. Browne

DOI: 10.1007/BF02294416

Cite this article as:
Browne, M.W. Psychometrika (1992) 57: 469. doi:10.1007/BF02294416


Structural models that yield circumplex inequality patterns for the elements of correlation matrices are reviewed. Particular attention is given to a stochastic process defined on the circle proposed by T. W. Anderson. It is shown that the Anderson circumplex contains the Markov Process model for a simplex as a limiting case when a parameter tends to infinity.

Anderson's model is intended for correlation matrices with positive elements. A replacement for Anderson's correlation function that permits negative correlations is suggested. It is shown that the resulting model may be reparametrzed as a factor analysis model with nonlinear constraints on the factor loadings. An unrestricted factor analysis, followed by an appropriate rotation, is employed to obtain parameter estimates. These estimates may be used as initial approximations in an iterative procedure to obtain minimum discrepancy estimates.

Practical applications are reported.

Key words

circumplex covariance structures correlation structures factor analysis simplex 

Copyright information

© The Psychometric Society 1992

Authors and Affiliations

  • Michael W. Browne
    • 1
  1. 1.Department of PsychologyThe Ohio State UniversityColumbusU.S.A.

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