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On finite mixtures of Discretized Beta model for ordered responses

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  • Rosaria Simone

    (University of Naples Federico II: Universita degli Studi di Napoli Federico II)

Abstract

The paper discusses the specification of finite mixture models based on the Discretized Beta distribution for the analysis of ordered discrete responses, as ratings and count data. The ultimate goal of the paper is to parameterize clusters of opposite and intermediate response outcomes. After a thorough discussion on model interpretation, identifiability and estimation, the proposal is illustrated on the wake of a case study on the probability to vote for German Political Parties and with a comparative discussion with the state of the art.

Suggested Citation

  • Rosaria Simone, 2022. "On finite mixtures of Discretized Beta model for ordered responses," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 828-855, September.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:3:d:10.1007_s11749-022-00800-7
    DOI: 10.1007/s11749-022-00800-7
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    References listed on IDEAS

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    1. Benedicte Apouey, 2007. "Measuring health polarization with self‐assessed health data," Health Economics, John Wiley & Sons, Ltd., vol. 16(9), pages 875-894, September.
    2. Mauro Mussini, 2018. "On Measuring Polarization For Ordinal Data: An Approach Based On The Decomposition Of The Leti Index," Statistics in Transition New Series, Polish Statistical Association, vol. 19(2), pages 277-296, June.
    3. Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    4. Rosaria Simone & Gerhard Tutz, 2018. "Modelling uncertainty and response styles in ordinal data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 224-245, August.
    5. Alison L. Gibbs & Francis Edward Su, 2002. "On Choosing and Bounding Probability Metrics," International Statistical Review, International Statistical Institute, vol. 70(3), pages 419-435, December.
    6. Pragya Sur & Galit Shmueli & Smarajit Bose & Paromita Dubey, 2015. "Modeling Bimodal Discrete Data Using Conway-Maxwell-Poisson Mixture Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(3), pages 352-365, July.
    7. Rosaria Simone, 2021. "An accelerated EM algorithm for mixture models with uncertainty for rating data," Computational Statistics, Springer, vol. 36(1), pages 691-714, March.
    8. David C. Blest, 2003. "A New Measure of Kurtosis Adjusted for Skewness," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 45(2), pages 175-179, June.
    9. Leonardo Grilli & Carla Rampichini & Roberta Varriale, 2015. "Binomial Mixture Modeling of University Credits," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(22), pages 4866-4879, November.
    10. Domenico Piccolo & Rosaria Simone, 2019. "Rejoinder to the discussion of “The class of cub models: statistical foundations, inferential issues and empirical evidence”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 477-493, September.
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    Cited by:

    1. Janette Larney & Gerrit Lodewicus Grobler & James Samuel Allison, 2022. "Introducing Two Parsimonious Standard Power Mixture Models for Bimodal Proportional Data with Application to Loss Given Default," Mathematics, MDPI, vol. 10(23), pages 1-19, November.
    2. Rosaria Simone, 2023. "Uncertainty Diagnostics of Binomial Regression Trees for Ordered Rating Data," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 79-105, April.
    3. Francesca Iorio & Riccardo Lucchetti & Rosaria Simone, 2024. "Testing distributional assumptions in CUB models for the analysis of rating data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(3), pages 669-701, September.

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