Psychometrika

, Volume 22, Issue 4, pp 325–345 | Cite as

Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space

  • Roger N. Shepard
Article

Abstract

A mathematical model is developed in an attempt to relate errors in multiple stimulus-response situations to psychological inter-stimulus and inter response distances. The fundamental assumptions are (a) that the stimulus and response confusions go on independently of each other, (b) that the probability of a stimulus confusion is an exponential decay function of the psychological distance between the stimuli, and (c) that the probability of a response confusion is an exponential decay function of the psychological distance between the responses. The problem of the operational definition of psychological distance is considered in some detail.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Attneave, F. Dimensions of similarity.Amer. J. Psychol., 1950,63, 516–556.Google Scholar
  2. [2]
    Blumenthal, L. M. Theory and applications of distance geometry. Oxford: Clarendon Press, 1953.Google Scholar
  3. [3]
    Brown, J. S., Bilodeau, E. A., and Baron, M. R. Bidirectional gradients in the strength of a generalized voluntary response to stimuli on a visual-spatial dimension.J. exp. Psychol., 1951,41, 52–61.Google Scholar
  4. [4]
    Busemann, H. The geometry of geodesics. New York: Academic Press, 1955.Google Scholar
  5. [5]
    Bush, R. R. and Mosteller, F. A model for stimulus generalization and discrimination.Psychol. Rev., 1951,58, 413–423.Google Scholar
  6. [6]
    Bush, R. R. and Mosteller, F. Stochastic models for learning. New York: Wiley, 1955.Google Scholar
  7. [7]
    Duncan, C. P. Development of response generalization gradients.J. exp. Psychol., 1955,50, 26–30.Google Scholar
  8. [8]
    Estes, W. K. Towards a statistical theory of learning.Psychol. Rev., 1950,57, 94–107.Google Scholar
  9. [9]
    Frick, F. C. An analysis of an operant discrimination.J. Psychol., 1948,26, 93–123.Google Scholar
  10. [10]
    Gibson, E. J. Sensory generalization with voluntary reactions.J. exp. Psychol., 1939,24, 237–253.Google Scholar
  11. [11]
    Gulliksen, H. and Wolfle, D. L. A theory of learning and transfer: I.Psychometrika, 1938,3, 127–149.Google Scholar
  12. [12]
    Guttman, N. and Kalish, H. I. Discriminability and stimulus generalization.J. exp. Psychol., 1956,51, 79–88.Google Scholar
  13. [13]
    Hovland, C. I. The generalization of conditioned responses: I. The sensory generalization of conditioned responses with varying frequencies of tone.J. gen. Psychol., 1937,17, 125–148.Google Scholar
  14. [14]
    Hovland, C. I. Human learning and retention. In S. S. Stevens (Ed.), Handbook of experimental psychology. New York: Wiley, 1951.Google Scholar
  15. [15]
    Hull, C. L. Principles of behavior. New York: Appleton-Century, 1943.Google Scholar
  16. [16]
    Kelley, J. L. General topology. New York: Van Nostrand, 1955.Google Scholar
  17. [17]
    Messick, S. J. Some recent theoretical developments in multidimensional scaling.Educ. psychol. Measmt, 1956,16, 82–100.Google Scholar
  18. [18]
    Messick, S. J. and Abelson, R. P. The additive constant problem in multidimensional scaling.Psychometrika, 1956,12, 1–15.Google Scholar
  19. [19]
    Margolius, G. Stimulus generalization of an instrumental response as a function of the number of reinforced trials.J. exp. Psychol., 1955,49, 105–111.Google Scholar
  20. [20]
    Noble, M. E. and Bahrick, H. P. Response generalization as a function of intratask response similarity.J. exp. Psychol., 1956,51, 405–412.Google Scholar
  21. [21]
    Pillsbury, W. B. A study in apperception.Amer. J. Psychol., 1897,8, 315–393.Google Scholar
  22. [22]
    Plotkin, L. Stimulus generalization in Morse code learning.Arch. Psychol., 1943,40, No. 287.Google Scholar
  23. [23]
    Rosenbaum, G. Stimulus generalization as a function of level of experimentally induced anxiety.J. exp. Psychol., 1953,45, 35–43.Google Scholar
  24. [24]
    Thurstone, L. L. Multiple-factor analysis. Chicago: Univ. Chicago Press, 1947.Google Scholar
  25. [25]
    Torgerson, W. S. Multidimensional scaling: I. Theory and method.Psychometrika, 1952,17, 401–420.Google Scholar
  26. [26]
    Woodworth, R. S. and Schlosberg, H. Experimental psychology. New York: Holt, 1955.Google Scholar
  27. [27]
    Young, G. and Householder, A. S. Discussion of a set of points in terms of their mutual distances.Psychometrika, 1938,3, 19–22.Google Scholar

Copyright information

© Psychometric Society 1957

Authors and Affiliations

  • Roger N. Shepard
    • 1
  1. 1.Naval Research LaboratoryUSA

Personalised recommendations