, Volume 59, Issue 1, pp 97–110 | Cite as

Similarities derived from 3-d nonlinear psychophysics: Variance distributions



Many-one mappings between stimulus properties and pairwise generated similarities are intrinsic to definitions of similarity. This of itself is not sufficient as a basis for predicting the variance associated with any single similarity judgment. An extension to cover this has to be made either by making ancillary assumptions about noise, or by using nonlinear models. The derivation of the variance of similarity judgments is made from the 3Γ process in nonlinear psychophysics. The idea of separability of dimensions in metric space theories of similarity is replaced by one parameter which represents the degree of a form of interdimensional crosscoupling

Key words

psychophysics similarity nonlinear dynamics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ashby, F. G., & Lee, W. W. (1991). Predicting similarity and categorization from indentification.Journal of Experimental Psychology: General, 120, 150–172.Google Scholar
  2. Broderson, U. (1968).Intra- und interindividuelle mehrdimensionale Skalierung eines nach objektiven Kriterien variierten Reizmaterials. Unpublished doctoral dissertation, University of Kiel.Google Scholar
  3. Campbell, E. A., & Gregson, R. A. M. (1990). Julia sets for the gamma recursion in nonlinear psychophysics.Acta Applicandae Mathematicae, 20, 177–188.Google Scholar
  4. Eisler, H., & Ekman, G. A. (1959). A mechanism of subjective similarity.Nordisk Psychologi, 11, 1–10.Google Scholar
  5. Eisler, H., & Lindman, R. (1990). Representations of dimensional models of similarity. In H.-G. Geissler, M. H. Müller, & W. Prinz (Eds.),Psychophysical explorations of mental structures (pp. 165–171). Göttingen: Hogrefe and Huber.Google Scholar
  6. Erickson, G. J., & Smith, C. R. (Eds.). (1988).Maximum entropy and Bayesian methods in science. Boston: Kluwer.Google Scholar
  7. Garner, W. R. (1974).The processing of information and structure. Potomac, MD: Lawrence Erlbaum Associates.Google Scholar
  8. Gregson, R. A. M. (1975).Psychometrics of similarity. New York: Academic Press.Google Scholar
  9. Gregson, R. A. M. (1976). A comparative study of seven similarity models.British Journal of Mathematical and Statistical Psychology, 29, 139–156.Google Scholar
  10. Gregson, R. A. M. (1980). Model evaluation via stochastic parameter convergence as on-line system identification.British Journal of Mathematical and Statistical Psychology, 33, 17–35.Google Scholar
  11. Gregson, R. A. M. (1985). Vergleich einiger mengentheoretischer und distanz-Repräsentation der Änlichkeitsdaten von Broderson (1968).Zeitschrift für experimentelle und angewandte Psychologie, 32, 573–587.Google Scholar
  12. Gregson, R. A. M. (1988).Nonlinear psychophysical dynamics. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  13. Gregson, R. A. M. (1989). A nonlinear systems approach to Fechner's paradox.Biological Cybernetics, 61, 129–138.Google Scholar
  14. Gregson, R. A. M. (1992a).n-Dimensional Nonlinear Psychophysics. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  15. Gregson, R. A. M. (1992b). The psychophysical method of limits: What happens in a nonlinear context?British Journal of Mathematical and Statistical Psychology, 45, 177–196.Google Scholar
  16. Gregson, R. A. M. (1993a). Minimum Boltzman entropy and the identification ofn-dimensional psychophysics.Proceedings of the Second Australian Cognitive Science Conference (pp. 82–84). Melbourne: University of Melbourne.Google Scholar
  17. Gregson, R. A. M. (1993b). Learning in the context of nonlinear psychophysics: The gamma zak embedding.British Journal of Mathematical and Statistical Psychology, 46, 31–48.Google Scholar
  18. Gregson, R. A. M. (in preparation).Theoretical isosimilarity contours derived from nonlinear psychophysics.Google Scholar
  19. Gregson, R. A. M., & Britton, L. A. (1990). The size-weight illusion in 2-D nonlinear psychophysics.Perception and Psychophysics, 48, 343–356.Google Scholar
  20. Gumbel, E. J. (1958).Statistics of extremes. New York: Columbia University Press.Google Scholar
  21. Krumhansl, C. L. (1978). Concerning the applicability of geometric models to similarity data; the interrelationship between similarity and spatial density.Psychological Review, 85, 445–463.Google Scholar
  22. Lingoes, J. C., & Roskam, E. E. (1973). A mathematical and empirical analysis of two multidimensional scaling algorithms.Psychometrika Monograph Supplement 38, 4(2), 1–81.Google Scholar
  23. Nosofsky, R. M. (1992). Similarity scaling and cognitive process models.Annual Review of Psychology, 43, 25–54.Google Scholar
  24. Nosofsky, R. M., & Smith, J. E. K. (1992). Similarity, identification and categorization: Comments on Ashby and Lee (1991).Journal of Experimental Psychology: General, 121, 237–245.Google Scholar
  25. Poulton, E. C. (1989).Bias in quantifying judgments. Hove: Lawrence Erlbaum Associates.Google Scholar
  26. Price, I. R., & Gregson, R. A. M. (1988). Nonlinear dynamics in a complex cubic one-dimensional model for sensory psychophysics.Acta Applicandae Mathematicae, 11, 1–17.Google Scholar
  27. Shepard, R. N. (1974). Representation of structure in similarity data: Problems and prospects.Psychometrika, 39, 373–421.Google Scholar
  28. Shepard, R. N. (1991). Integrability versus separability of stimulus dimensions: From an early convergence of evidence to a proposed theoretical basis. In G. R. Lockhead & J. R. Pomerantz (Eds.),The perception of structure (pp. 53–72). Washington, DC: American Psychological Association.Google Scholar
  29. Tversky, A. (1977). Features of similarity.Psychological Review, 84, 327–352.Google Scholar
  30. Tversky, A., & Gati, I. (1982). Similarity, separability, and the triangle inequality.Psychological Review, 89, 123–154.Google Scholar
  31. Vanagas, V. (1991). Activeness of the recognition process: Possible methods of investigation.Eksperimentine Biologija (Vilnius), 2(6), 3–18.Google Scholar
  32. Young, F. W. (1970). Nonmetric multidimensional scaling: Recovery of metric information.Psychometrika, 35, 455–473.Google Scholar

Copyright information

© The Psychometric Society 1994

Authors and Affiliations

  1. 1.Department of PsychologyAustralian National UniversityCanberraAustralia

Personalised recommendations