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Analysis of cross classified data by AIC

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Summary

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.

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References

  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. Akaike, H. (1976). On entropy maximization principle,Applications of Statistics, P. R. Krishnaiah, ed., North-Holland, Amsterdam, 27–41.

    Google Scholar 

  3. Bishop, Y. M. M. (1969). Full contingency tables, logits and split contingency tables,Biometrics,25, 383–400.

    Article  Google Scholar 

  4. Darroch, J. N. (1962). Interactions in multifactor contingency tables,J. R. Statist. Soc., B24, 251–263.

    MATH  Google Scholar 

  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. 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. Sakamoto, Y. (1974). A study of the Japanese National Character—Part V.Ann. Inst. Statist. Math., Supplement 8, 1–58.

    Google Scholar 

  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. Wermuth, N. (1976). Analogies between multiplicative models in contingency tables and covariance analysis.Biometrics,32, 95–108.

    Article  MathSciNet  Google Scholar 

  10. Wermuth, N. (1976). Model search among multiplicative models,Biometrics,32, 253–263.

    Article  MathSciNet  Google Scholar 

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Authors
  1. Yosiyuki Sakamoto
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  2. Hirotugu Akaike
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The Institute of Statistical Mathematics

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Sakamoto, Y., Akaike, H. Analysis of cross classified data by AIC. Ann Inst Stat Math 30, 185–197 (1978). https://doi.org/10.1007/BF02480213

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  • DOI: https://doi.org/10.1007/BF02480213

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