Annals of the Institute of Statistical Mathematics

, Volume 30, Issue 1, pp 185–197

Analysis of cross classified data by AIC

  • Yosiyuki Sakamoto
  • Hirotugu Akaike


The purpose of the present paper is to propose a simple but practically useful procedure for the analysis of multidimensional contingency tables of survey data. By the procedure we can determine the predictor on which a specific variable has the strongest dependence and also the optimal combination of predictors. The procedure is very simply realized by the search for the minimum of the statistic AIC within a set of models proposed in this paper. The practical utility of the procedure is demonstrated by the results of some successful applications to the analysis of the survey data of the Japanese national character. The difference between the present procedure and the conventional test procedure is briefly discussed.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle,2nd International Symposium on Information Theory, B. N. Petrov and F. Csaki, Eds., Akademiai Kiado, Budapest, 267–281.Google Scholar
  2. [2]
    Akaike, H. (1976). On entropy maximization principle,Applications of Statistics, P. R. Krishnaiah, ed., North-Holland, Amsterdam, 27–41.Google Scholar
  3. [3]
    Bishop, Y. M. M. (1969). Full contingency tables, logits and split contingency tables,Biometrics,25, 383–400.CrossRefGoogle Scholar
  4. [4]
    Darroch, J. N. (1962). Interactions in multifactor contingency tables,J. R. Statist. Soc., B24, 251–263.MATHMathSciNetGoogle Scholar
  5. [5]
    Goodman, L. A. (1970). The multivariate analysis of qualitative data: interactions among multiple classifications,J. Amer. Statist. Ass.,65, 225–256.Google Scholar
  6. [6]
    Research Committee on the Study of Japanese National Character (1976).Nipponjin no Kokuminsei, sono san (A study of the Japanese National Character, Part III), Shiseido, Tokyo. (In Japanese)Google Scholar
  7. [7]
    Sakamoto, Y. (1974). A study of the Japanese National Character—Part V.Ann. Inst. Statist. Math., Supplement 8, 1–58.Google Scholar
  8. [8]
    Sakamoto, Y. (1977). A model for the optimal pooling of categories of the predictor in a contingency table,Research Memorandum, No. 119, The Institute of Statistical Mathematics, Tokyo.Google Scholar
  9. [9]
    Wermuth, N. (1976). Analogies between multiplicative models in contingency tables and covariance analysis.Biometrics,32, 95–108.MATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    Wermuth, N. (1976). Model search among multiplicative models,Biometrics,32, 253–263.MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1978

Authors and Affiliations

  • Yosiyuki Sakamoto
  • Hirotugu Akaike

There are no affiliations available

Personalised recommendations