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Assessing Similarity of Rating Distributions by Kullback-Leibler Divergence

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Classification and Multivariate Analysis for Complex Data Structures

Abstract

A mixture model for ordinal data modelling (denoted CUB) has been recently proposed in literature. Specifically, ordinal data are represented by means of a discrete random variable which is a mixture of a Uniform and shifted Binomial random variables. This article proposes a testing procedure based on the Kullback-Leibler divergence in order to compare CUB models and detect similarities in the structure of judgements that raters express on set of items.

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References

  1. Agresti, A.: Categorical Data Analysis, 2nd ed. Wiley, New York, NY (2002)

    Book  MATH  Google Scholar 

  2. Arabie, P., Hubert, L.J.: The bond energy algorithm revisited. IEEE Trans. Syst. Man Cybern. 20, 268–274 (1990)

    Article  Google Scholar 

  3. Cerchiello P., Iannario M., Piccolo D.: Assessing risk perception by means of ordinal models. In: Perna C., et al. (eds.) Mathematical and Statistical Methods for Insurance and Finance, pp. 65–73. Verlag, Berlin (2010)

    Google Scholar 

  4. Climer, S., Zhang, W.: Rearrangement clustering: Pitfalls, remedies and applications. J. Mach. Learn. 7, 919–943 (2006)

    MathSciNet  Google Scholar 

  5. D’Elia, A., Piccolo, D.: A mixture model for preference data analysis. Comput. Stat. Data Anal. 49, 917–934 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. D’Elia, A., Piccolo, D.: Uno studio sulla percezione delle emergenze metropolitane: un approccio modellistico. Quad. Stat. 7, 121–161 (2005)

    Google Scholar 

  7. Healy, N.: Analysis of RIDDOR machinery accidents in the UK printing and publishing industries 2003–2004. Health Safety Laboratory. HSL/2006/83, Buxton, Derbyshire, UK (2006)

    Google Scholar 

  8. Kullback, S.: Information Theory and Statistics. Dover Publications, New York, NY (1959)

    MATH  Google Scholar 

  9. Kupperman, M.: Further Applications of Information Theory to Multivariate Analysis and Statistical Inference. George Washington University, Washington, DC (1957)

    Google Scholar 

  10. McCormick, W.T., Schweitzer, P.J., White, T.W.: Problem decomposition and data reorganization by a clustering technique. Oper. Res. 20, 993–1009 (1972)

    Article  MATH  Google Scholar 

  11. McCullagh, P., Nelder, J.A.: Generalized Linear Models. Chapman & Hall, London (1989)

    MATH  Google Scholar 

  12. McCullagh, P.: Regression models for ordinal data. J. R. Stat. Soc. Ser. B 42, 109–142 (1980)

    MathSciNet  MATH  Google Scholar 

  13. Piccolo, D., D’Elia, A.: A new approach for modelling consumers’ preferences. Food Qual. Prefer. 19, 247–259 (2008)

    Article  Google Scholar 

  14. Piccolo, D.: Observed information matrix for MUB models. Quad. Stat. 8, 33–78 (2006)

    Google Scholar 

  15. Piccolo, D.: On the moments of a mixture of uniform and shifted Binomial random variables. Quad. Stat. 5, 86–104 (2003)

    Google Scholar 

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Acknowledgments

This research was partly funded by the MIUR-PRIN 2006 grant (Project on: “Stima e verifica di modelli statistici per l’analisi della soddisfazione degli studenti universitari”) and CFEPSR (Portici, NA).

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Correspondence to Marcella Corduas .

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Corduas, M. (2011). Assessing Similarity of Rating Distributions by Kullback-Leibler Divergence. In: Fichet, B., Piccolo, D., Verde, R., Vichi, M. (eds) Classification and Multivariate Analysis for Complex Data Structures. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13312-1_22

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