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Similarities Derived from 3-d Nonlinear Psychophysics: Variance Distributions

Published online by Cambridge University Press:  01 January 2025

Robert A. M. Gregson
Robert A. M. Gregson*
Affiliation:
Australian National University, Canberra
*
Requests for reprints should be sent to Robert A. M. Gregson, Department of Psychology, Australian National University, Canberra, ACT 0200 AUSTRALIA. Source code in Fortran is available via email: [email protected].
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Abstract

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

Keywords

psychophysicssimilaritynonlinear dynamics
Type
Article
Information
Psychometrika , Volume 59 , Issue 1 , March 1994 , pp. 97 - 110
Copyright
Copyright © 1994 The Psychometric Society

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References

Ashby, F. G., Lee, W. W. (1991). Predicting similarity and categorization from indentification. Journal of Experimental Psychology: General, 120, 150–172.CrossRefGoogle Scholar
Broderson, U. (1968). Intra- und interindividuelle mehrdimensionale Skalierung eines nach objektiven Kriterien variierten Reizmaterials. Unpublished doctoral dissertation, University of Kiel.Google Scholar
Campbell, E. A., Gregson, R. A. M. (1990). Julia sets for the gamma recursion in nonlinear psychophysics. Acta Applicandae Mathematicae, 20, 177–188.CrossRefGoogle Scholar
Eisler, H., Ekman, G. A. (1959). A mechanism of subjective similarity. Nordisk Psychologi, 11, 1–10.CrossRefGoogle Scholar
Eisler, H., Lindman, R. (1990). Representations of dimensional models of similarity. In Geissler, H.-G., Müller, M. H., Prinz, W. (Eds.), Psychophysical explorations of mental structures (pp. 165–171). Göttingen: Hogrefe and Huber.Google Scholar
Erickson, G. J., Smith, C. R. (1988). Maximum entropy and Bayesian methods in science, Boston: Kluwer.Google Scholar
Garner, W. R. (1974). The processing of information and structure, Potomac, MD: Lawrence Erlbaum Associates.Google Scholar
Gregson, R. A. M. (1975). Psychometrics of similarity, New York: Academic Press.Google Scholar
Gregson, R. A. M. (1976). A comparative study of seven similarity models. British Journal of Mathematical and Statistical Psychology, 29, 139–156.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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
Gregson, R. A. M. (1988). Nonlinear psychophysical dynamics, Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
Gregson, R. A. M. (1989). A nonlinear systems approach to Fechner's paradox. Biological Cybernetics, 61, 129–138.CrossRefGoogle ScholarPubMed
Gregson, R. A. M. (1992). n-Dimensional Nonlinear Psychophysics, Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
Gregson, R. A. M. (1992). The psychophysical method of limits: What happens in a nonlinear context?. British Journal of Mathematical and Statistical Psychology, 45, 177–196.CrossRefGoogle Scholar
Gregson, R. A. M. (1993). Minimum Boltzman entropy and the identification of n-dimensional psychophysics (pp. 82–84). Melbourne: University of Melbourne.Google Scholar
Gregson, R. A. M. (1993). Learning in the context of nonlinear psychophysics: The gamma zak embedding. British Journal of Mathematical and Statistical Psychology, 46, 31–48.CrossRefGoogle Scholar
Gregson, R. A. M. (in preparation). Theoretical isosimilarity contours derived from nonlinear psychophysics.Google Scholar
Gregson, R. A. M., Britton, L. A. (1990). The size-weight illusion in 2-D nonlinear psychophysics. Perception and Psychophysics, 48, 343–356.CrossRefGoogle ScholarPubMed
Gumbel, E. J. (1958). Statistics of extremes, New York: Columbia University Press.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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
Nosofsky, R. M. (1992). Similarity scaling and cognitive process models. Annual Review of Psychology, 43, 25–54.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Poulton, E. C. (1989). Bias in quantifying judgments, Hove: Lawrence Erlbaum Associates.Google Scholar
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.CrossRefGoogle Scholar
Shepard, R. N. (1974). Representation of structure in similarity data: Problems and prospects. Psychometrika, 39, 373–421.CrossRefGoogle Scholar
Shepard, R. N. (1991). Integrability versus separability of stimulus dimensions: From an early convergence of evidence to a proposed theoretical basis. In Lockhead, G. R., Pomerantz, J. R. (Eds.), The perception of structure (pp. 53–72). Washington, DC: American Psychological Association.Google Scholar
Tversky, A. (1977). Features of similarity. Psychological Review, 84, 327–352.CrossRefGoogle Scholar
Tversky, A., Gati, I. (1982). Similarity, separability, and the triangle inequality. Psychological Review, 89, 123–154.CrossRefGoogle ScholarPubMed
Vanagas, V. (1991). Activeness of the recognition process: Possible methods of investigation. Eksperimentine Biologija (Vilnius), 2(6), 3–18.Google Scholar
Young, F. W. (1970). Nonmetric multidimensional scaling: Recovery of metric information. Psychometrika, 35, 455–473.CrossRefGoogle Scholar