A multivariate rate equation for variable-interval performance

Abstract

A value-like parameter is introduced into a rate equation for describing variable-interval performance. The equation, derived solely from formal considerations, expresses rate of responding as a joint function of rate of reinforcement and "reinforcer power." Preliminary tests of the rate equation show that it handles univariate data as well as Herrnstein's hyperbola. In addition, a form of Herrnstein's hyperbola can be derived from the equation, and it predicts forms of matching in concurrent situations. For the multivariate case, reinforcer values scaled in concurrent situations where matching is assumed to hold are taken as determinations of reinforcer power. The multivariate rate equation is fitted to an appropriate set of data and found to provide a good description of variable-interval performance when both rate and power of reinforcement are varied. Rate and power measures completely describe reinforcement. The effects of their joint variation are not predicted and cannot be described by Herrnstein's equation.