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A multivariate rate equation for variable-interval performance.

J J McDowell, R Kessel

    Journal of the Experimental Analysis of Behavior
    |March 1, 1979
    PubMed
    Summary
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    A new rate equation for variable-interval performance incorporates "reinforcer power," improving predictions beyond Herrnstein's hyperbola. This model better describes how both the rate and power of reinforcement jointly affect behavior.

    Area of Science:

    • Behavioral psychology
    • Mathematical modeling of behavior

    Background:

    • Herrnstein's hyperbola is a key model for understanding response rate as a function of reinforcement rate.
    • Existing models may not fully capture the complex interplay of reinforcement variables.

    Purpose of the Study:

    • Introduce a novel rate equation incorporating a "reinforcer power" parameter.
    • To describe variable-interval performance as a joint function of reinforcement rate and power.
    • To test the equation's predictive accuracy against existing models and data.

    Main Methods:

    • Derivation of a new rate equation from formal considerations.
    • Testing the equation with univariate data, comparing it to Herrnstein's hyperbola.
    • Deriving a form of Herrnstein's hyperbola from the new equation to predict concurrent performance.

    Related Experiment Videos

  • Scaling reinforcer values in concurrent situations to determine reinforcer power.
  • Fitting the multivariate rate equation to empirical data with varied reinforcement rate and power.
  • Main Results:

    • The new rate equation accurately describes univariate data, matching Herrnstein's hyperbola.
    • A derived form of the equation predicts matching in concurrent situations.
    • The multivariate equation provides a good description of variable-interval performance when both reinforcement rate and power are varied.
    • The proposed model accounts for the joint effects of reinforcement rate and power, which are not predicted by Herrnstein's equation.

    Conclusions:

    • The introduced "reinforcer power" parameter, alongside reinforcement rate, offers a more complete description of reinforcement.
    • The new rate equation provides a superior framework for understanding and predicting behavior under variable-interval schedules, especially when reinforcement characteristics vary.
    • This model advances the quantitative analysis of behavior by integrating multiple facets of reinforcement.