Abstract
When multidimensional scaling solutions are used to study semantic concepts, the dimensionality of the optimal configuration has to be determined. Several strategies have been proposed to choose the appropriate dimensionality. In the present paper, the traditional dimensionality choice criteria were evaluated and compared to a method based on the prediction of an external criterion. Two studies were conducted in which typicality of an exemplar within a semantic concept was predicted from its distance to the concept centroid. In contrast to the low-dimensional solutions selected by the traditional methods, predictions of an external criterion improved with additional dimensions up till dimensionalities that were much higher than what is common in the literature. This suggests that traditional methods underestimate the richness of semantic concepts as revealed in spatial representations derived from similarity measures.
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Akaike, H. (1974). A new look at the statistical model identification.IEEE: Transactions & Automatic Control,19, 716–723.
Ameel, E., &Storms, G. (2006). From prototypes to caricatures: Geometrical models for concept typicality.Journal of Memory & Language,55, 402–421.
Ameel, E., Storms, G., Malt, B. C., &Sloman, S. A. (2005). How bilinguals solve the naming problem.Journal of Memory & Language,53, 60–80.
Arnold, J. B. (1971). A multidimensional scaling study of semantic distance.Journal of Experimental Psychology,90, 349–372.
Ashby, F. G., &Gott, R. E. (1988). Decision rules in the perception and categorization of multidimensional stimuli.Journal of Experimental Psychology: Learning, Memory, & Cognition,14, 33–53.
Barsalou, L. W. (1990). On the indistinguishability of exemplar memory and abstraction in category representation. In T. K. Srull & R. S. Wyer (Eds.),Advances in social cognition: Content and process specificity in the effects of prior experiences (Vol. 3, pp. 61–88). Hillsdale, NJ: Erlbaum.
Borg, I., &Groenen, P. J. F. (1997). Modern multidimensional scaling. New York: Springer.
De Soete, G. (1983). A least squares algorithm for fitting additive trees to proximity data.Psychometrika,48, 621–626.
Gärdenfors, P. (2004).Conceptual spaces: The geometry of thought. Cambridge, MA: MIT Press.
Griffiths, T. L., &Steyvers, M. (2002). A probabilistic approach to semantic representation. In W. D. Gray, & C. D. Schunn (Eds.),Proceedings of the 24th Annual Conference of the Cognitive Science Society (pp. 381–386). Mahwah, NJ: Erlbaum.
Hampton, J. A. (1979). Polymorphous concepts in semantic memory.Journal of Verbal Learning & Verbal Behavior,18, 441–461.
Hampton, J. A. (1993). Prototype models of concept representations. In I. Van Mechelen, J. A. Hampton, R. S. Michalski, & P. Theuns (Eds.),Categories and concepts: Theoretical views and inductive data analysis (pp. 67–95). London: Academic Press.
Holyoak, K. J., &Walker, J. H. (1976). Subjective magnitude information in semantic orderings.Journal of Verbal Learning & Verbal Behavior,15, 287–299.
Jones, R. A., &Rosenberg, S. (1974). Structural representations of naturalistic descriptions of personality.Multivariate Behavioral Research,9, 218–230.
Komatsu, L. K. (1992). Recent Views of conceptual structure.Psychological Bulletin,112, 500–526.
Kruschke, J. K. (1992). ALCOVE: An exemplar-based connectionist model of category learning.Psychological Review,99, 22–44.
Kruskal, J. B. (1964). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis.Psychometrika,29, 1–27.
Kruskal, J. B., &Wish, M. (1978). Multidimensional scaling. Beverly Hills, CA: Sage.
Landauer, T. K., &Dumais, S. T. (1997). A solution to Plato’s problem: The latent semantic analysis theory of acquisition, induction, and representation of knowledge.Psychological Review,104, 211–240.
Lee, M. D. (2001). Determining the dimensionality of multidimensional scaling representations for cognitive modeling.Journal of Mathematical Psychology,45, 149–166.
Lund, K., &Burgess, C. (1996). Producing high-dimensional semantic spaces from lexical co-occurrence.Behavior Research Methods, Instruments, & Computers,28, 203–208.
Lund, K., &Burgess, C., &Atchley, R. A. (1995). Semantic and associative priming in high-dimensional semantic space. In J. D. Moore, & J. F. Lehman (Eds.),Proceedings of the 17th Annual Conference of the Cognitive Science Society (pp. 660–665). Hillsdale, NJ: Erlbaum.
McKinley, S. C., &Nosofsky, R. M. (1995). Investigations of exemplar and decision bound models in large, ill-defined category structures.Journal of Experimental Psychology: Human Perception & Performance,21, 128–148.
Medin, D. M., &Schaffer, M. M. (1978). Context theory of classification learning.Psychological Review,85, 207–238.
Medin, D. L., &Schwanenflugel, P. J. (1981). Linear separability in classification learning.Journal of Experimental Psychology: Human Learning & Memory,5, 355–368.
Nosofsky, R. M. (1984). Choice, similarity, and the context model of classification.Journal of Experimental Psychology: Learning, Memory, & Cognition,10, 104–114.
Nosofsky, R. M. (1986). Attention, similarity, and the identification-categorization relationship.Journal of Experimental Psychology: General,115, 39–57.
Pruzansky, S., Tversky, A., &Carroll, J. D. (1982). Spatial versus tree representations of proximity data.Psychometrika,47, 3–24.
Ramsay, J. O. (1977). Maximum likelihood estimation in multidimensional scaling.Psychometrika,42, 241–266.
Ramsay, J. O. (1980). Some small sample results for maximum likelihood estimation in multidimensional scaling.Psychometrika,45, 139–144.
Reed, S. K. (1972). Pattern recognition and categorization.Cognitive Psychology,3, 382–407.
Rips, L. J. (1975). Inductive judgments about natural categories.Journal of Verbal Learning & Verbal Behavior,14, 665–681.
Rips, L. J., Shoben, E. J., &Smith, E. E. (1973). Semantic distance and the verification of semantic relations.Journal of Verbal Learning & Verbal Behavior,12, 1–20.
Rosch, E., &Mervis, C. B. (1975). Family resemblances: Studies in the internal structure of categories.Cognitive Psychology,7, 573–605.
Rosenberg, S., &Jones, R. (1972). A method for investigating and representing a person’s implicit theory of personality: Theodore Dreiser’s view of people.Journal of Personality & Social Psychology,22, 372–386.
Ruts, W., De Deyne, S., Ameel, E., Van Paemel, W., Verbeemen, T., &Storms, G. (2004). Flemish norm data for 13 natural concepts and 343 exemplars.Behavior Research Methods, Instruments, & Computers,36, 506–515.
Ruts, W., Storms, G., &Hampton, J. (2004). Linear separability in superordinate natural language concepts.Memory & Cognition,32, 83–95.
SAS Institute Inc. (1999).SAS STAT Users’ Guide 8. Cary, NC: Author.
Schiffman, S. S., Reynolds, M. L., &Young, F. W. (1981).Introduction to multidimensional scaling: Theory, methods, and applications. New York: Academic Press.
Schwarz, G. (1978). Estimating the dimensions of a model.Annals of Statistics,6, 461–464.
Shepard, R. N., &Arabie, P. (1979). Additive clustering: Representation of similarities as combinations of discrete overlapping properties.Psychological Review,86, 87–123.
Shoben, E. J. (1976). The verification of semantic relations in a same-different paradigm: An asymmetry in semantic memory.Journal of Verbal Learning & Verbal Behavior,15, 365–379.
Shoben, E. J. (1983). Applications of multidimensional scaling in cognitive psychology.Applied Psychological Measurement,7, 473–490.
Shoben, E. J., &Ross, B. H. (1987). Structure and process in cognitive psychology using multidimensional scaling and related techniques. In R. R. Ronning, J. A. Glover, J. C. Conoley, & J. C. Witt (Eds.),The influence of cognitive psychology on testing. London: Erlbaum.
Smith, J. D., &Minda, J. P. (1998). Prototypes in the mist: The early epochs of category learning.Journal of Experimental Psychology: Learning, Memory, & Cognition,24, 1411–1436.
Smith, J. D., &Minda, J. P. (2000). Thirty categorization results in search of a model.Journal of Experimental Psychology: Learning, Memory, & Cognition,26, 3–27.
Smits, T., Storms, G., Rosseel, Y., &De Boeck, P. (2002). Fruits and vegetables categorized: An application of the generalized context model.Psychonomic Bulletin & Review,9, 836–844.
Spence, I. (1983). Monte Carlo simulation studies.Applied Psychological Measurement,7, 405–425.
Spence, I., &Graef, J. (1974). The determination of the underlying dimensionality of an empirically obtained matrix of proximities.Multivariate Behavioral Research,9, 331–341.
Steyvers, M., & Griffiths, T. L. (in press). Probabilistic topic models. In T. Landauer, D. McNamara, S. Dennis, & W. Kintsch (Eds.), Latent semantic analysis: A road to meaning. Mahwah, NJ: Erlbaum.
Storms, G. (1995). On the robustness of maximum likelihood scaling for violations of the error model.Psychometrika,60, 247–258.
Storms, G., Dirikx, T., Saerens, J., Verstraeten, S., &De Deyn, P. P. (2003). On the use of scaling and clustering in the study of semantic disruptions.Neuropsychology,17, 289–301.
Takane, Y. (1981). Multidimensional successive categories scaling: A maximum likelihood method.Psychometrika,46, 9–28.
Takane, Y., &Carroll, J. D. (1982). Nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities.Psychometrika,46, 389–405.
Tversky, A., &Hutchinson, W. (1986). Nearest-neighbor analysis of psychological spaces.Psychological Review,93, 3–22.
Wagenaar, W. A., &Padmos, P. (1971). Quantitative interpretation of stress in Kruskal’s multidimensional scaling technique.British Journal of Mathematical & Statistical Psychology,24, 101–110.
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The research presented in this paper was partly sponsored by grants OT/05/27 and IDO/02/004 of the Leuven University Research Council awarded to Gert Storms. The two first authors contributed equally to this manuscript. Eef Ameel is research assistant at the Fund for Scientific Research, Flanders.
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Verheyen, S., Ameel, E. & Storms, G. Determining the dimensionality in spatial representations of semantic concepts. Behavior Research Methods 39, 427–438 (2007). https://doi.org/10.3758/BF03193012
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DOI: https://doi.org/10.3758/BF03193012