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On the identifiability of a mixture model for ordinal data

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Summary

In this article we discuss the identifiability of a probability model which has been proven useful for capturing the main features of ordinal data generated by rating surveys. Specifically, we show that the mixture of a shifted Binomial and a Uniform discrete distribution is identifiable when the number of categories is greater than three.

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References

  • Atienza N., Garcia-Heras J. and Muñoz-Pichardo J. M. (2006) A new condition for identifiability of finite mixture distributions, Metrika, 63, 215–221.

    Article  MathSciNet  MATH  Google Scholar 

  • Balirano G. and Corduas M. (2008) Detecting semiotically expressed humor in diasporic TV productions, HUMOR: International Journal of Humor Research, 3, 227–251.

    Google Scholar 

  • Bock R. D. and Moustaki I. (2007) Item response theory in a general framework, In: Psychometrics, (eds. C. R. Rao and S. Sinharay), Handbook of Statistics 26,469-513.

  • Cappelli C. and D’Elia A. (2004) La percezione della sinonimia: un’analisi statistica mediante modelli per ranghi, In: Le poids des mots — Actes de JADT2004, (eds. Prunelle G., Fairon C. and Dister A.), Presses Universitaires de Louvain, Belgium, 229–240.

    Google Scholar 

  • Corduas M. (2008) A testing procedure for clustering ordinal data by cub models, Proceeding of the Joint SFC-CLADAG Meeting, ESI, Napoli, 245–248.

  • Corduas M., Iannario M. and Piccolo D. (2009) A class of statistical models for evaluating services and performances, In: Statistical Methods for the Evaluation of Educational Services and Quality of Products, (eds. M. Bini, P. Monari, D. Piccolo, L. Salmaso), Contribution to Statistics, Springer, 99–117.

  • D’Elia A. (2008) A statistical modelling approach for the analysis of TMD chronic pain data, Statistical Methods in Medical Research, 17, 389–403.

    Article  MathSciNet  MATH  Google Scholar 

  • D’Elia A. and Piccolo D. (2005) A mixture model for preference data analysis, Computational Statistics Data Analysis, 49, 917–934.

    Article  MathSciNet  MATH  Google Scholar 

  • Fruhwirth-Schnatter S. (2006) Finite Mixture and Markov Switching Models, Springer Series in Statistics, Springer, New York.

    Google Scholar 

  • Hennig C. (2000) Identifiability of models for clusterwise linear regression, Journal of Classification, 17, 273–296.

    Article  MathSciNet  MATH  Google Scholar 

  • Iann ario M. (2007) A statistical approach for modelling Urban Audit Perception Surveys, Quaderni di Statistica, 9, 149–172.

    Google Scholar 

  • Iannario M. (2010) Modelling shelter choices in ordinal surveys, submitted for publication.

  • Iannario M. and Piccolo D. (2009) A program in R for CUB models inference, Version 2.0, available at http://www.dipstat.unina.it

  • Iannario M. and Piccolo D. (2010) A new statistical model for the analysis of customer satisfaction, Quality Technology & Quantitative Management, 7, 149–168.

    Google Scholar 

  • McCullagh P. (1980) Regression models for ordinal data (with discussion), Journal of the Royal Statistical Society, Series B, 42, 109–142.

    MathSciNet  MATH  Google Scholar 

  • McCullagh P. and Nelder J. A. (1989) Generalized Linear Models, 2nd edition, Chapman and Hall, London.

    MATH  Google Scholar 

  • McLachlan G. and Peel G. J. (2000) Finite Mixture Models, J. Wiley & Sons, New York.

    Book  MATH  Google Scholar 

  • Piccolo D. (2003) On the moments of a mixture of uniform and shifted binomial random variables, Quaderni di Statistica, 5, 85–104.

    Google Scholar 

  • Piccolo D. (2006) Observed information matrix for MUB models, Quaderni di Statistica, 8, 33–78.

    Google Scholar 

  • Piccolo D. (2008) Modelling University students’ final grades by ordinal variables, Quaderni di Statistica, 10, 205–226.

    Google Scholar 

  • Piccolo D. and D’Elia A. (2008) A new approach for modelling consumers’ preferences, Food Quality and Preference, 19, 247–259.

    Article  Google Scholar 

  • Piccolo D. and Iannario M. (2008) Qualitative and quantitative models for ordinal data analysis, Proceedings of MTISD 2008, Methods, Models and Information Technologies for Decision Support Systems, Università del Salento, Lecce, 140–143.

  • Teicher H. (1963) Identifiability of finite mixtures, The Annals of Mathematical Statistics, 34,1265–1269.

    Article  MathSciNet  MATH  Google Scholar 

  • Titterington D.M., Smith A.F.M. and Makov U.E. (1985) Statistical Analysis of Finite Mixture Distributions, J. Wiley & Sons, New York.

    MATH  Google Scholar 

  • Yakowitz S. J. and Spragins J. D. (1968) On the identifiability of finite mixtures, The Annals of Mathematical Statistics, 39, 209–214.

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Maria Iannario.

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Iannario, M. On the identifiability of a mixture model for ordinal data. METRON 68, 87–94 (2010). https://doi.org/10.1007/BF03263526

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  • DOI: https://doi.org/10.1007/BF03263526

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