Marc Scholten (*)

Pedro Zany Caldeira (**)

RESUMO

Este artigo fornece uma introdução ao escalonamento multidimensional (MultiDimensional Scaling - MDS), um conjunto de modelos de distância espacial como forma de representação de dados de proximidade. O artigo focaliza-se no que é que o MSD faz, no sentido de que tipo de representações produz a partir de um conjunto de dados de proximidade, e no que é que o investigador deve fazer para que o MDS faça, no sentido de que tipo de métodos de recolha e de preparação de dados se deve usar de modo a obter dados que permitem a análise de MDS. O artigo ignora em grande parte a matéria técnica de como é que o MDS faz, embora forneça directivas para ajudar o investigador decidir se se justifica ajustar um modelo de distâncias espaciais aos dados de proximidade obtidos, escolher entre os modelos principais e as opções de modelos na análise de dados e conseguir uma interpretação válida dos resultados do MDS.

Palavras-chave: Dados de Proximidade, Escalonamento Multidimensional.

This article provides an introduction to MultiDimensional Scaling (MDS) as it refers to a family of spatial-distance models for the representation of proximity data. The article focuses on what MDS does, in the sense of what type of representations it produces given a set of proximity data, and what the researcher has to do in order to make MDS do it, in the sense of what type od data-collection and data-preparation methods are to be used in order to obtain data that are amenable to MDS analysis. The article largely ignores the technical matter of how MDS does it, although it provides guidelines to aid the research in deciding whether it is justifiable to fit a spatial-distance model to the proximity data obtained, choosing among the principal models and model options in data analysis, and reahing a valid interpretation of the MDS results.

Key words: Proximity Data, MultiDimensional (MDS).

Texto completo disponível apenas em PDF.

Full text only available in PDF format.

REFERÊNCIAS

Bennett, J. F., & Hays, W. L. (1960). Multidimensional unfolding: Determining the dimensionality of ranked preference data. Psychometrika, 25, 27-43.         [ Links ]

Burton, M. L. (1975). Dissimilarity measures for unconstrained sorting data. Multivariate Behavioral Research, 10, 409-424.

Carroll, J. D. (1972). Individual differences and multidimensional scaling. In A. K. Romney, R. N. Shepard, & S. B. Nerlove (Eds.), Multidimensional scaling (Vol. 1, pp. 105-155). New York: Seminar Press.

Carroll, J. D., & Arabie, P. (1980). Multidimensional scaling. Annual Review of Psychology, 31, 607-649.

Carroll, J. D., & Chang, J. J. (1970). Analysis of individual differences in multidimensional scaling via an N-Way generalization of Eckart-Young decomposition. Psychometrika, 35, 283-319.

Carroll, J. D., Green, P. E., & Schaffer, C. M. (1986). Interpoint distance comparisons in correspondence analysis. Journal of Marketing Research, 23, 271-280.

Carroll, J. D., Wish, M. (1974a). Models and methods for three-way multidimensional scaling. In R. C. Atkinson, D. H. Krantz, R. D. Luce, & P. Suppes (Eds.), Contemporary developments in mathematical psychology. Measurement, psychophysics, and neural information processing (Vol. 2, pp. 57-105). San Francisco: W.H. Freeman.

Carroll, J. D., Wish, M. (1974b). Multidimensional perceptual models and measurement methods. In E. C. Carterette, & M. P. Friedman (Eds.), Handbook of perception. Psychophysical judgment and measurement (Vol. 2, pp. 391-447). New York: Academic Press.

Coombs, C. H. (1950). Psychological scaling without a unit of measurement. Psychological Review, 57, 148-158.

Coombs, C. H. (1964). A theory of data. New York: John Wiley.

Cronbach, L. J., & Gleser, G. C. (1953). Assessing similarity between profiles. Psychological Bulletin, 50, 456-473.

Davison, M. L. (1983). Multidimensional scaling. New York: John Wiley.

Green, P. E., Carmone, F. J., Smith, S. M. (1987). Multidimensional scaling: Concepts and Applications. Boston: Allyn & Bacon.

Green, P. E., Maheshwari, A., & Rao, V. R. (1969). Dimensional Interpretation and configuration invariance in multidimensional scaling: An empirical study. Multivariate Behavioral Research, 4 (2), 159-180.

James, W. (1890). The principles of psychology. New York: Henry Holt & Co.

Jones, L. E., & Koehly, L. M. (1993). Multidimensional scaling. In G. Keren & C. Lewis (Eds.), A handbook for data analysis in the behavioral sciences: Methodological Issues (pp. 95-163). Hillsdale: Lawrence Erlbaum.

Krumhansl, C. L. (1978). Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85 (5), 445-463.

Kruskal, J. B. (1964a). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1-27.

Kruskal, J. B. (1964b). Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29, 115-129.

Nickerson, R. S. (1972). Binary-classification reaction time: A review of some studies of human informa-tion-processing capabilities. Psychonomic Monograph Supplements, 4, 275-317.

Osgood, C. E., Suci, G., & Tannenbaum, P. H. (1957). The measurement of meaning. Urbana: University of Illinois Press.

Richardson, M.W. (1939). Multidimensional psychophysics. Psychological Bulletin, 35, 659-660.

Rosenberg, S., Nelson, C., & Vivekananthan, P. S. (1968). A multidimensional approach to the structure of personality impressions. Journal of Personality and Social Psychology, 9 (4), 283-294.

Rosenberg, S., & Kim, M. P. (1975). The method of sorting as a data-gathering procedure in multivariate research. Multivariate Behavioral Research, 10, 489-502.

Schiffman, S. S., Reynolds, M. L., & Young, F. W. (1981). Introduction to multidimensional scaling. Theory, methods, and applications. Orlando: Academic Press.

Schönemann, P. H. (1972). An algebraic solution for a class of subjective metrics models. Psychometrika, 37, 441-451.

Shepard, R. N. (1957). Stimulus and response generalization: A stochastic model relating generalization to distance in psychological space. Psychometrika, 22, 325-345.

Shepard, R. N. (1962a). Analysis of proximities: Multidimensional scaling with an unknown distance function. I. Psychometrika, 27, 125-140.

Shepard, R. N. (1972). A taxonomy of some principal types of data and of multi-dimensional methods for their analysis. In R. N. Shepard, A. K. Romney, & S. B. Nerlove (Eds.), Multidimensional scaling. Theory and applications in the behavioral sciences (Vol. 1, pp. 21-47). New York: Seminar Press.

Skinner, H. A. (1978). Differentiating the contribution of elevation, scatter and shape in profile similarity. Educational and Psychological Measurement, 38, 297-308.

Smith, E. E., & Medin, D. L. (1981). Categories and concepts. Cambridge: Harvard University Press.

Spence, I., & Domoney, D.W. (1974). Single subject incomplete designs for nonmetric multi-dimen-sional scaling. Psychometrika, 39, 469-490.

Torgerson, W. S. (1958). Theory and methods of scaling. New York: John Wiley.

Tversky, A. (1977). Features of similarity. Psychological Review, 84 (4), 327-352.

Wish, M. (1970). Comparisons among multidimensional structures of nations based on different measures of subjective similarity. In L. von Bertalanffy, & A. Rapoport (Eds.), General systems (Vol. 15, pp. 55-65). Washington: Society for General Systems Research.

Wish, M. (1976). Comparisons among multidimensional structures of interpersonal relations. Multivariate Behavioral Research, 11, 297-324.

(**) Bolseiro PRAXIS XXI/UIIPOG-ISPA.