Homogeneity Analysis for Partitioning Qualitative Variables

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


This paper proposes a method to construct multiple uni-dimensional scales by partitioning qualitative variables into mutually exclusive groups. The method is based on homogeneity analysis, and fuzzy c-means criterion is introduced for partitioning. Also, some goodness of fit indexes are proposed. Two artificial data sets and one real data set are analyzed as numerical examples. The results illustrate that the proposed method is more effective for partitioning qualitative variables compared with PCA with optimal scaling and Hayashi’s Quantification Method III or HOMALS.


Global Minimum Qualitative Variable Multiple Correspondence Analysis Artificial Data Score Vector 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bezdek, J.C. (1981): Pattern Recognition with Fuzzy Objective Function Algorithm. Plenum Press, New York.CrossRefGoogle Scholar
  2. Gifi, A. (1990): Non Linear Multivariate Analysis. John Wiley and Sons, Chichester.Google Scholar
  3. Kendall, M.G.(1983): The Advanced Theory of Statistics, Volume, 3,.4th ed. Charles Griffin.Google Scholar
  4. MacQueen, J. (1967): Some methods for classification and analysis of multivariate observations. Proceeding of the fifth Berkeley Symposium on Mathematical Statistics and Probability, 1, 281–297.MathSciNetGoogle Scholar
  5. Meulmann, J.J. (1996): Fitting a distance model to homogeneous subsets of variables: points of view analysis of categorical data. Journal of Classification, 13, 249–267.CrossRefGoogle Scholar
  6. Sato, T. and Yanai, H. (1985): A method of simultaneous scaling of discrete variables. Behaviormetrika, 18, 39–51.CrossRefGoogle Scholar

Copyright information

© Springer Japan 1998

Authors and Affiliations

  • Takahiro Tsuchiya
    • 1
  1. 1.The Institute of Statistical MathematicsMinato-ku, Tokyo 106Japan

Personalised recommendations