Solutions to some nonlinear equations from nonmetric data

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.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.