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A comprehensive framework of regression models for ordinal data

Author

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  • Maria Iannario

    (University of Naples Federico II)

  • Domenico Piccolo

    (University of Naples Federico II)

Abstract

Literature on the models for ordinal variables grew very fast in the last decades and several proposals have been advanced when ordered data are expression of ratings, preferences, judgments, opinions, etc. A dichotomy has been emphasized between methods based on a latent variable which is behind the ordered selection and methods anchored to a probability distribution with a well defined pattern. In this paper, a comprehensive framework to regression models is proposed in case ordinal data come out from a discrete choice. The added value of this unifying perspective is the possibility to introduce further generalizations and also to deepen similarities and differences among the proposed models. A case study confirms the usefulness of this general framework. Some concluding remarks end the paper.

Suggested Citation

  • Maria Iannario & Domenico Piccolo, 2016. "A comprehensive framework of regression models for ordinal data," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 233-252, August.
    • Handle: RePEc:spr:metron:v:74:y:2016:i:2:d:10.1007_s40300-016-0091-x
    DOI: 10.1007/s40300-016-0091-x
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    References listed on IDEAS

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    1. Kim, Ji-Hyun, 2003. "Assessing practical significance of the proportional odds assumption," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 233-239, November.
    2. Greene, William H. & Hensher, David A., 2003. "A latent class model for discrete choice analysis: contrasts with mixed logit," Transportation Research Part B: Methodological, Elsevier, vol. 37(8), pages 681-698, September.
    3. Michel Wedel & Wayne DeSarbo, 1995. "A mixture likelihood approach for generalized linear models," Journal of Classification, Springer;The Classification Society, vol. 12(1), pages 21-55, March.
    4. Richard Breen & Ruud Luijkx, 2010. "Mixture Models for Ordinal Data," Sociological Methods & Research, , vol. 39(1), pages 3-24, August.
    5. Domenico Piccolo, 2015. "Inferential Issues on CUBE Models with Covariates," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(23), pages 5023-5036, December.
    6. D'Elia, Angela & Piccolo, Domenico, 2005. "A mixture model for preferences data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 917-934, June.
    7. Maria Iannario, 2015. "Detecting latent components in ordinal data with overdispersion by means of a mixture distribution," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 977-987, May.
    8. Miller, Gregory K. & Fridell, Stephanie L., 2007. "A Forgotten Discrete Distribution? Reviving the Negative Hypergeometric Model," The American Statistician, American Statistical Association, vol. 61, pages 347-350, November.
    9. Bettina Grün & Friedrich Leisch, 2008. "Identifiability of Finite Mixtures of Multinomial Logit Models with Varying and Fixed Effects," Journal of Classification, Springer;The Classification Society, vol. 25(2), pages 225-247, November.
    10. Anna Gottard & Maria Iannario & Domenico Piccolo, 2016. "Varying uncertainty in CUB models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 10(2), pages 225-244, June.
    11. Bercedis Peterson & Frank E. Harrell, 1990. "Partial Proportional Odds Models for Ordinal Response Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(2), pages 205-217, June.
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    2. Ribecco, Nunziata & D'Uggento, Angela Maria & Labarile, Angela, 2022. "What influences the perception of immigration in Italian adolescents? An analysis with CUB models for rating data," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    3. Simone, Rosaria & Tutz, Gerhard & Iannario, Maria, 2020. "Subjective heterogeneity in response attitude for multivariate ordinal outcomes," Econometrics and Statistics, Elsevier, vol. 14(C), pages 145-158.
    4. M. Meleddu & M. Pulina & G. Solinas & S. Capecchi, 2019. "Mixture models for consumers' preferences in healthcare," Working Paper CRENoS 201901, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.

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