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On the Analysis of Over-Dispersed Categorical Data

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Modern Quantification Theory

Part of the book series: Behaviormetrics: Quantitative Approaches to Human Behavior ((BQAHB,volume 8))

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Abstract

In Chaps. 7 and  8, our focus has been on describing some of the technical aspects of reciprocal averaging (and canonical correlation analysis), so that one can obtain row and column scores that maximize the association between the variables of a two-way contingency table. The foundations under which, such discussions are laid, rests upon the assumption that the cell frequencies of the contingency table are assumed to be Poisson random variables. This is apparent by observing that for the \(\left( i,\,j\right) \)th cell it is defined \(Z_{ij}\).

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References

  • Agresti, A. (2013). Categorical Data Analysis (3rd ed.). New York: Wiley.

    Google Scholar 

  • Beh, E. (2012). Simple correspondence analysis using adjusted residuals. Journal of Statistical Planning and Inference, 142, 965–973.

    Article  MathSciNet  Google Scholar 

  • Beh, E., & Lombardo, R. (2020a). Five strategies for accommodating overdispersion in simple correspondence analysis. In Imaizumi, T., Okada, A., Miyamoto, S., Sakaori, F., Y. Yamamoto, Y., & Vichi, M., (Eds.), Advanced Studies in Classification and Data Science. Studies in Classification, Data Analysis, and Knowledge Organization (pp. 117–129). Singapore: Springer.

    Google Scholar 

  • Beh, E., Lombardo, R., & Alberti, G. (2018). Correspondence analysis and the freeman-tukey statistic: A study of archaeological data. Computational Statistics and Data Analysis, 128, 73–86.

    Article  MathSciNet  Google Scholar 

  • Beh, E. J., & Lombardo, R. (2014). Correspondence analysis: Theory practice and new strategies. Chichester: Wiley.

    Google Scholar 

  • Beh, E. J., & Lombardo, R. (2020b). An introduction to correspondence analysis. Chichester (in press): Wiley.

    Google Scholar 

  • Consul, P. (1989). Generalized poisson distributions: Properties and applications. New York: Marcel Dekker.

    Google Scholar 

  • Consul, P. C., & Jain, G. C. (1973). A generalization of the Poisson distribution. Technometrics, 15, 791–799.

    Article  MathSciNet  Google Scholar 

  • Conway, R. W., & Maxwell, W. (1962). A queuing model with state dependent service rates. Journal of Industrial Engineering, 12, 132–136.

    Google Scholar 

  • Efron, B. (1992). Over dispersion estimates based on the method of asymmetric maximum likelihood. Journal of the American Statistical Association, 87, 98–107.

    Article  MathSciNet  Google Scholar 

  • Fisher, R. A. (1941). The negative binomial distribution. Annals of Eugenics, 11, 182–187.

    Article  MathSciNet  Google Scholar 

  • Freeman, M. F., & Tukey, J. W. (1950). Transformations related to the angular and square root. The Annals of Mathematical Statistics, 21, 607–611.

    Article  MathSciNet  Google Scholar 

  • Garmize, L. M., & Rychlak, J. F. (1964). Role-play validation of a sociocultural theory of symbolism. Journal of Consulting Psychology, 28, 107–115.

    Article  Google Scholar 

  • Haberman, S. (1973). The analysis of residuals in cross-classified tables. Biometrics, 75, 457–467.

    Google Scholar 

  • Nishisato, S. (1984). Forced classification: A simple application of a quantification method. Psychometrika, 49(1), 25–36.

    Article  Google Scholar 

  • Nishisato, S. (1985). Methods for handling outlier responses in dual scaling. In Proceedings of the 49th Annual Meeting of the Japanese Psychological Association, (p. 50)?

    Google Scholar 

  • Nishisato, S. (1987). Robust techniques for quantifying categorical data. In MacNeil, B. & Umphrey, G. J., (Eds.), Foundations of statistical inference. (pp. 209–217). Dordrecht: D. Reidel Publishing.

    Google Scholar 

  • Nishisato, S. (1991). Standardizing multidimensional space for dual scaling. In Proceedings of the 20th Annual Meeting of the German Operations Research Society, Hohenheim University, (pp. 584–591).

    Google Scholar 

  • Sellers, K. F., Borle, S., & Schmueli, G. (2012). The COM-Poisson model for count data: A survey of methods and applications. Applied Stochastic Models in Business and Industry, 28, 104–116.

    Article  MathSciNet  Google Scholar 

  • Shmueli, G., Minka, T. P., Kadane, J. B., Borle, S., & Boatwright, P. (2005). A useful distribution for fitting discrete data: Revival of the conway-maxwell-poisson distribution. Applied Statistics, 54, 127–142.

    MathSciNet  MATH  Google Scholar 

  • Tripathi, R. C., & Gupta, R. C. (1984). Statistical inference regarding the generalized Poisson distribution. Sankhya (Series B), 46, 166–173.

    MathSciNet  MATH  Google Scholar 

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Correspondence to Shizuhiko Nishisato .

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Nishisato, S., Beh, E.J., Lombardo, R., Clavel, J.G. (2021). On the Analysis of Over-Dispersed Categorical Data. In: Modern Quantification Theory. Behaviormetrics: Quantitative Approaches to Human Behavior, vol 8. Springer, Singapore. https://doi.org/10.1007/978-981-16-2470-4_11

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