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Solutions to Some Nonlinear Equations from Nonmetric Data

Published online by Cambridge University Press:  01 January 2025

Stanley J. Rule
Stanley J. Rule*
Affiliation:
University of Alberta
*
Request for reprints should be sent to Stanely J. Rule, Department of Psychology, University of Alberta, Edmonton, Alberta, CANADA, T6G 2E9.
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Abstract

A method is presented to provide estimates of parameters of specified nonlinear equations from ordinal data generated from a crossed design. The analytic method, NOPE, is an iterative method in which monotone regression and the Gauss-Newton method of least squares are applied alternatively until a measure of stress is minimized. Examples of solutions from artificial data are presented together with examples of applications of the method to experimental results.

Keywords

monotone regressionGauss-Newton methodordinal dataparameter estimation
Type
Original Paper
Information
Psychometrika , Volume 44 , Issue 2 , June 1979 , pp. 143 - 155
Copyright
Copyright © 1979 The Psychometric Society

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Footnotes

This work was begun while the author was on sabbatical leave during 1970-71 at the Department of Mathematical Psychology, University of Nijmegen, the Netherlands, where discussions with E. E. Roskam on the problem were very helpful. Support was provided by Grant A0151 from the Natural Sciences and Engineering Council, Canada.

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