Skip to main content
SpringerLink
Log in

Multidimensional scaling models for reaction times and same-different judgments

  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

A method for joint analysis of reaction times and same-different judgments is discussed. A set of stimuli is assumed to have some parametric representation which uniquely defines dissimilarities between the stimuli. Those dissimilarities are then related to the observed reaction times and same-different judgments through a model of psychological processes. Three representation models of dissimilarities are considered, the Minkowski power distance model, the linear model, and Tversky's feature matching model. Maximum likelihood estimation procedures are developed and implemented in the form of a FORTRAN program. An example is given to illustrate the kind of analyses that can be performed by the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Reference notes

  • Ramsay, J. O. Some models for similarity. A paper presented at the European meeting of the Psychometric Society, Groningen, The Netherlands, 1980.

  • Furnas, G. W. Personal communication.

  • Kruskal, J. B. Personal communication.

  • Koopman, R. F., & Cooper, M. Some problems with Minkowski distance models in multidimensional scaling. Paper presented at the Psychometric Society meeting, Stanford, 1974.

  • Sergent, J. & Takane, Y. Structures in two-choice reaction time data. A manuscript in preparation.

References

  • Akaike, H. A new look at the statistical model identification.IEEE Transactions on Automatic Control, 1974,19, 716–723.

    Google Scholar 

  • Arabie, P. & Carroll, J. D. MAPCLUS: a mathematical programming approach to fitting the ADCLUS model.Psychometrika, 1980,45, 211–235.

    Google Scholar 

  • Attneave, F. Dimensions of similarity.American Journal of Psychology, 1950,63, 516–556.

    Google Scholar 

  • Carroll, J. D. & Chang, J. J. Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition.Psychometrika, 1970,35, 283–319.

    Google Scholar 

  • Chocholle, R. Variation des temps de reaction auditifs en fonction de l'intensite a diverses frequences.L'Annee Psychologique, 1940,41, 65–124.

    Google Scholar 

  • Coombs, C. H.A theory of data. New York: Wiley, 1964.

    Google Scholar 

  • Curtis, D. W., Paulos, M. A., & Rule, S. J. Relation between disjunctive reaction time and stimulus difference.Journal of Experimental Psychology, 1973,99, 167–173.

    Google Scholar 

  • Davies, G. M., Ellis, H. D., & Shepherd, J. W. Cue saliency in faces as assessed by the “Photofit” technique.Perception, 1977,6, 263–269.

    Google Scholar 

  • Ellis, H. D. Recognising faces.British Journal of Psychology, 1975,66, 409–426.

    Google Scholar 

  • Fishburn, P. C. Lexicographic additive differences.Journal of Mathematical Psychology, 1980,21, 191–218.

    Google Scholar 

  • Garner, W. R. Aspects of a stimulus: Features, dimensions, and configurations. In E. Rosch & B. B. Lloyd (Eds.),Cognition and Categorization. Hillsdale, N.J.: Erlbaum, 1978.

    Google Scholar 

  • Green, D. M. & Swets, J. A.Signal detection theory and psychophysics. New York: Krieger, 1966.

    Google Scholar 

  • Grice, G. R., Nullmeyer, R. & Spiker, V. A. Application of variable criterion theory to choice reaction time.Perception & Psychophysics, 1977,22, 431–449.

    Google Scholar 

  • Hefner, R. A. Extensions of the law of comparative judgement to discriminable and multidimensional stimuli. Unpublished doctoral dissertation, University of Michigan, 1958.

  • Hyman, R. & Well, A. Judgment of similarity and spatial models.Perception & Psychophysics, 1967,2, 233–248.

    Google Scholar 

  • Hyman, R. & Well, A. Perceptual separability and spatial models.Perception & Psychophysics, 1968,3, 161–165.

    Google Scholar 

  • Ida, M. The application of the Weibull distribution to the analysis of the reaction time data.Japanese Psychological Research, 1980,22, 207–212.

    Google Scholar 

  • Johnson, N. L. & Kotz, S.Distributions in statistics: Continuous univariate distributions—I. Boston: Houghton Mifflins, 1970.

    Google Scholar 

  • Johnson, S. C. Hierarchical clustering scheme.Psychometrika, 1967,32, 241–254.

    Google Scholar 

  • Keren, G. & Baggen, S. Recognition models of alphanumeric characters.Perception & Psychophysics, 1981,29, 234–246.

    Google Scholar 

  • Krueger, L. E. A theory of perceptual matching.Psychological Review, 1978,85, 278–304.

    Google Scholar 

  • Krumhansl, C. L. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density.Psychological Review, 1978,84, 445–463.

    Google Scholar 

  • Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis.Psychometrika, 1964a,29, 1–29.

    Google Scholar 

  • Kruskal, J. B. Nonmetric multidimensional scaling: a numerical method.Psychometrika, 1964b,29, 115–129.

    Google Scholar 

  • LaBerge, D. A recruitment theory of simple behavior.Psychometrika, 1962,27, 375–396.

    Google Scholar 

  • Laming, D.Mathematical Psychology. London: Academic Press, 1973.

    Google Scholar 

  • Link, S. W. Applying RT deadlines to discrimination reaction time.Psychonomic Science, 1971,25, 355–358.

    Google Scholar 

  • Link, S. W. The relative judgment theory of two choice response time.Journal of Mathematical Psychology, 1975,12, 114–136.

    Google Scholar 

  • Link, S. W. & Tindall, A. D. Speed and accuracy in comparative judgments of line length.Perception & Psychophysics, 1971,9, 284–288.

    Google Scholar 

  • Lockhead, G. R. Processing dimensional stimuli: a note.Psychological Review, 1972,79, 410–419.

    Google Scholar 

  • Lockhead, G. R. Holistic versus analytic process models: A reply.Journal of Experimental Psychology: Human Perception and Performance, 1979,5, 746–755.

    Google Scholar 

  • Lord, F. M. & Novick, M. R.Statistical theories of mental test scores. Menlo Park, Calif.: Addision-Wesley, 1968.

    Google Scholar 

  • Marley, A. A. J. Multivariate stochastic processes compatible with “aspect” models of similarity and choice.Psychometrika, 1981,46, 421–428.

    Google Scholar 

  • McGill, W. J. & Gibbon, J. The general gamma distribution and reaction times.Journal of Mathematical Psychology, 1965,2, 1–18.

    Google Scholar 

  • Medin, D. L. & Schaffer, M. M. Context theory of classification learning.Psychological Review, 1978,85, 207–238.

    Google Scholar 

  • Miller, J. Multidimensional same-different judgments: evidence against independent comparisons of dimensions.Journal of Experimental Psychology: Human Perception and Performance, 1978,4, 411–422.

    Google Scholar 

  • Monahan, J. S. & Lockhead, G. R. Identification of integral stimuli.Journal of Experimental Psychology: General, 1977,196, 94–110.

    Google Scholar 

  • Nickerson, R. S. Same-different reaction times with multi-attribute stimulus differences.Perceptual and Motor Skills, 1967,24, 543–554.

    Google Scholar 

  • Nickerson, R. S. Binary-classification reaction time: a review of some studies of human information-processing capabilities.Psychonomic Monograph Supplements, 1972,4, 275–318.

    Google Scholar 

  • Ollman, R. Fast guesses in choice reaction time.Psychonomic Science, 1966,6, 155–156.

    Google Scholar 

  • Petrusic, W. M. & Jamieson, D. G. Relation between probability of preferential choice and time to choose changes with practice.Journal of Experimental Psychology: Human Perception and Performance, 1978,4, 471–482.

    Google Scholar 

  • Podgorny, P. Deciding that objects are the same. Unpublished doctoral dissertation, Yale University, 1980.

  • Podgorny, P. and Garner, W. R. Reaction time as a measure of inter- and intraobject visual similarity: letters of the alphabet.Perception & Psychophysics, 1979,26, 37–52.

    Google Scholar 

  • Posner, M. I.Chronometric Explorations of Mind. Hillsdale, N.J. Erlbaum, 1978.

    Google Scholar 

  • Ramsay, J. O. Maximum likelihood estimation in multidimensional scaling.Psychometrika, 1977,42, 241–266.

    Google Scholar 

  • Ramsay, J. O. Confidence regions for multidimensional scaling analysis.Psychometrika, 1978,43, 145–160.

    Google Scholar 

  • Ramsay, J. O. Joint analysis of direct ratings, pairwise preferences and dissimilarities.Psychometrika, 1980,45, 149–165.

    Google Scholar 

  • Ramsay, J. O. Some statistical approaches to multidimensional scaling.Journal of the Royal Statistical Society, Series A, 1982.

  • Restle, F.Psychology of judgment and choice. New York: Wiley, 1961.

    Google Scholar 

  • Rock, I.Orientation and form. New York: Academic Press, 1973.

    Google Scholar 

  • Sergent, J. About face: Left-hemisphere involvement in processing physiognomies.Journal of Experimental Psychology: Human Perception and Performance, 1982,8, 1–14.

    Google Scholar 

  • Sergent, J. & Bindra, D. Differential hemispheric processing of faces: methodological considerations and reinterpretation.Psychological Bulletin, 1981,89, 541–554.

    Google Scholar 

  • Shepard, R. N. The analysis of proximities: multidimensional scaling with an unknown distance function, I & II.Psychometrika, 1962,27, 125–140 & 219–246.

    Google Scholar 

  • Shepard, R. N. Attention and the metric structure of the stimulus space.Journal of Mathematical Psychology, 1964,1, 54–87.

    Google Scholar 

  • Shepard, R. N. Representation of structure in similarity data: problems and prospects.Psychometrika, 1974,39, 373–421.

    Google Scholar 

  • Shepard, R. N. The circumplex and related topological manifolds in the study of perception. In Shye, S. (Ed.),Theory construction and data analysis in the social sciences. San Francisco: Jossey-Bass, 1978.

    Google Scholar 

  • Shepard, R. N. & Arabie, P. Additive clustering: Representation of similarities as combinations of discrete overlapping properties.Psychological Review, 1979,86, 87–123.

    Google Scholar 

  • Shepard, R. N., Kilpatric, D. W. & Cunningham, J. P. The internal representation of numbers.Cognitive Psychology, 1975,7, 82–138.

    Google Scholar 

  • Sorkin, R. D. Extension of the theory of signal detectability to matching procedures in psychoacoustics.The Journal of Acoustic Society of America, 1962,34, 1745–1751.

    Google Scholar 

  • Stone, M. Models for choice-reaction time.Psychometrika, 1960,25, 251–260.

    Google Scholar 

  • Takane, Y. A maximum likelihood method for nonmetric multidimensional scaling: I. The case in which all empirical pairwise orderings are independent—theory and evaluations.Japanese Psychological Research, 1978,20, 7–17 and 105–114.

    Google Scholar 

  • Takane, Y. Multidimensional successive categories scaling: a maximum likelihood method.Psychometrika, 1981,46, 9–28.

    Google Scholar 

  • Takane, Y. Maximum likelihood additivity analysis.Psychometrika, 1982,47, 225–241.

    Google Scholar 

  • Takane, Y. & Carroll, J. D. Nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities.Psychometrika, 1981,46, 389–405.

    Google Scholar 

  • Torgerson, W. S.Theory and methods of scaling. New York: Wiley, 1958.

    Google Scholar 

  • Tversky, A. Features of similarity.Psychological Review, 1977,84, 327–352.

    Google Scholar 

  • Winsberg, S., & Ramsay, J. O. Analysis of pairwise preference data using integrated B-splines.Psychometrika, 1981,46, 171–186.

    Google Scholar 

  • Yellot, J. I. Correction for fast guessing and the speed-accuracy trade-off in choice reaction time.Journal of Mathematical Psychology, 1971,8, 159–199.

    Google Scholar 

  • Young, F. W. Nonmetric scaling of line length using latencies, similarity, and same-different judgments.Perception & Psychophysics, 1970,8, 363–369.

    Google Scholar 

  • Young, F. W., de Leeuw, J., & Takane, Y. Quantifying qualitative data. In Lantermann, E. D., and Feger, H. (Eds.)Similarity and choice. Vienna: Hans Huber, 1980.

    Google Scholar 

  • Zinnes, J. L., & Wolff, R. P. Single and multidimensional same-different judgments.Journal of Mathematical Psychology, 1977,16, 30–50.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Psychology, McGill University, 1205 Avenue Docteur Penfield, H3A 1B1, Montreal, Quebec, Canada

    Yoshio Takane & Justine Sergent

Authors
  1. Yoshio Takane
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Justine Sergent
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The work reported in this paper is supported by Grant A6394 to the first author from the Natural Sciences and Engineering Research Council of Canada. Portions of this study have been presented at the Psychometric Society meeting in Chapel Hill, N.C., in May, 1981. We thank Tony Marley, Jim Ramsay and anonymous reviewers for their helpful comments. MAXRT, a computer program which performs the computations described in this paper may be obtained by writing to the first author.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Takane, Y., Sergent, J. Multidimensional scaling models for reaction times and same-different judgments. Psychometrika 48, 393–423 (1983). https://doi.org/10.1007/BF02293683

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02293683

Key words

Search

Navigation