Exploring Multidimensional Quantification Space

  • Shizuhiko Nishisato
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


Dual scaling deals with two distinct types of categorical data, incidence data and dominance data. While perfect row-column association of an incidence data matrix does not mean that the data matrix can be fully explained by one solution, dominance data with perfect association can be explained by one solution. Considering a main role of quantification theory is to explain data in multidimensional space, the present study presents a non-technical look at some fundamental aspects of quantification space that are used for analysis of the two types of data.


Principal Component Analysis Incidence Data Multiple Correspondence Analysis Principal Component Analysis Result Quantification Space 
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  1. Carroll, J.D. (1972). Individual differences and multidimensional scaling. In R.N. Shepard, A.K. Romney, and S.B. Nerlove (eds.), Multidimensional Scaling: Theory and Applications in the Behavioral Sciences, Volume 1. New York: Seminar Press.Google Scholar
  2. Coombs, C.H. (1950). Psychological scaling without a unit of measurement. Psychological Review, 57, 148–158.CrossRefGoogle Scholar
  3. Coombs, C.H. (1964). A Theory of Data. New York: Wiley.Google Scholar
  4. Coombs, C.H., and Rao, R.C. (1960). On a connection between factor analysis and multidimensional unfolding. Psychometrika, 25, 219–231.MATHCrossRefGoogle Scholar
  5. Gold, E.M. (1973). Metric unfolding: Data requirements for unique solution and clarification of Schönemann’s algorithm. Psychometrika. 38, 555–569.MathSciNetMATHCrossRefGoogle Scholar
  6. Greenacre, M.J., and Browne, M.W. (1986). An efficient alternating least-squares algorithm to perform multidimensional unfolding. Psychornetrika, 51, 241–250.MATHCrossRefGoogle Scholar
  7. Heiser, W.J. (1981). Unfolding analysis of proximity data. Doctoral dissertation, Leiden University, The Netherlands.Google Scholar
  8. Nishisato, S. (1978). Optimal scaling of paired comparison and rank-order data: An alternative to Guttman’s formulation. Psychometrika, 43, 263–271.MATHCrossRefGoogle Scholar
  9. Nishisato, S. (1980). Analysis of Categorical Data: Dual Scaling and Its Applications. Toronto: University of Toronto Press.MATHGoogle Scholar
  10. Nishisato, S. (1993). On quantifying different types of categorical data. Psychometrika, 58, 617–629.MATHCrossRefGoogle Scholar
  11. Nishisato, S. (1994). Elements of Dual Scaling: An Introduction to Practical Data Analysis. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  12. Nishisato. S. (1996). Gleaning in the field of dual scaling. Psychometrika, 61, 559–599.MATHCrossRefGoogle Scholar
  13. Nishisato, S., and Yamauchi, H. Principal components of deviation scores and standardized scores. Japanese Psychological Research, 16, 162–170.Google Scholar
  14. Schönemann, P.H. (1970). On metric multidimensional unfolding. Psychometrika, 35, 167–176.Google Scholar
  15. Schönemann; P.H., and Wang, M.M. (1972). An individual difference model for the multidimensional analysis of preference data. Psychometrika, 37, 2 75–309.CrossRefGoogle Scholar
  16. Torgerson, W.S. (1958). Theory and Methods of Scaling. New York: Wiley.Google Scholar

Copyright information

© Springer Japan 1998

Authors and Affiliations

  • Shizuhiko Nishisato
    • 1
  1. 1.OISE/UTThe University of TorontoToronto, OntarioCanada

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