, Volume 40, Issue 4, pp 525–548

Nonlinear programming approach to optimal scaling of partially ordered categories

  • Shizuhiko Nishisato
  • P. S. Arri

DOI: 10.1007/BF02291554

Cite this article as:
Nishisato, S. & Arri, P.S. Psychometrika (1975) 40: 525. doi:10.1007/BF02291554


A modified technique of separable programming was used to maximize the squared correlation ratio of weighted responses to partially ordered categories. The technique employs a polygonal approximation to each single-variable function by choosing mesh points around the initial approximation supplied by Nishisato's method. The major characteristics of this approach are: (i) it does not require any grid refinement; (ii) the entire process of computation quickly converges to the acceptable level of accuracy, and (iii) the method employs specific sets of mesh points for specific variables, whereby it reduces the number of variables for the separable programming technique. Numerical examples were provided to illustrate the procedure.

Copyright information

© Psychometric Society 1975

Authors and Affiliations

  • Shizuhiko Nishisato
    • 1
  • P. S. Arri
  1. 1.The Ontario Institute for Studies in EducationCanada