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Rejoinder to the discussion of “The class of cub models: statistical foundations, inferential issues and empirical evidence”

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Abstract

The paper is the rejoinder to a series of Discussions on the class of cub models for rating data. The main topics advanced by Discussants are reviewed and debated, with focus on the most prominent issues. As a result, the trailhead of possible future research developments is outlined.

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References

  • Agresti A (2010) Analysis of ordinal categorical data, 2nd edn. Wiley, Hoboken

    Book  MATH  Google Scholar 

  • Angelini V, Cavapozzi D, Corazzini L, Paccagnella O (2014) Do Danes and Italians rate life satisfaction in the same way? Using vignettes to correct for individual-specific scale biases. Oxf Bull Econ Stat 76(5):643–666

    Article  Google Scholar 

  • Arboretti R, Bordignon P (2016) Consumer preferences in food packaging: CUB models and conjoint analysis. Br Food J 118(3):527–540

    Article  Google Scholar 

  • Bandt C (2005) Ordinal time series analysis. Ecol Model 182:229–238

    Article  Google Scholar 

  • Bandt C, Shiha F (2007) Order patterns in time series. J Time Ser Anal 28:646–65

    Article  MathSciNet  MATH  Google Scholar 

  • Bartolucci F, Bacci S, Gnaldi M (2015) Statistical analysis of questionnaires: a unified approach based on R and Stata. Chapman & Hall/CRC, Boca Raton

    Book  MATH  Google Scholar 

  • Benzécri J (1973) L’Analyse des Donnés. L’Analyse des Correspondances. Dunod publisher, Tome II

  • Biernacki C, Jacques J (2016) Model-based clustering of multivariate ordinal data relying on a stochastic binary search algorithm. Stat Comput 26(5):929–943

    Article  MathSciNet  MATH  Google Scholar 

  • Birnbaum A (1968) Some latent traits models and their use in inferring an examinee’s ability. In: Lord FM, Novick MR (eds) Statistical theories of mental test scores. Addison-Wesley, Reading, pp 395–479

    Google Scholar 

  • Capecchi S, Michelini M (2018) Aprototype for the analysis of time use in Italy. In: Abbruzzo A, Brentari E, Chiodi M, Piacentino D (eds) Book of short papers SIS 2018. Pearson Publisher, London, pp 487–492. ISBN-9788891910233

  • Capecchi S, Simone R (2019) A proposal for a model-based composite indicators: experience on perceived discrimination in Europe. Soci Ind Res 141(1):95–110

    Article  Google Scholar 

  • Capecchi S, Endrizzi I, Gasperi F, Piccolo D (2016) A multi-product approach for detecting subjects’ and objects’ covariates in consumer preferences. Br Food J 118(3):515–526

    Article  Google Scholar 

  • Capecchi S, Meleddu M, Pulina M, Solinas G (2019) Mixture models for consumers’ preferences in healthcare, CRENoS Working Papers 1, Centro Ricerche Economiche Nord Sud, Cagliari-Sassari, Arkadia Editore, Cagliari, ISBN 9788884678355

  • Corduas M (2008a) Clustering cub models by Kullback–Liebler divergence. In: Proceedings of SCF-CLAFAG Meeting, ESI, Napoli, pp 245–248

  • Corduas M (2008b) A statistical procedure for clustering ordinal data. Quad Stat 10:177–189

    Google Scholar 

  • Corduas M (2011a) A study on University students’ opinions about teaching quality: a model based approach to clustering ordinal data. In: Attanasio M, Capursi V (eds) Statistical methods for the evaluation of university systems. Springer, Berlin, pp 67–78

    Chapter  Google Scholar 

  • Corduas M (2011b) Assessing similarity of rating distributions by Kullback–Liebler divergence. In: Fichet A et al (eds) Classification and multivariate analysis for complex data structures, studies in classification, data analysis, and knowledge organization. Springer, Berlin, pp 221–228

    Google Scholar 

  • Davino C, Simone R, Vistocco D (2018). Exploring synergy between CUB models and quantile regression: a comparative analysis through continuousized data. In: Capecchi S, Di Iorio F, Simone R (eds) Proceedings of the international conference ASMOD 2018. Federico II University Press, Naples, pp 101–108. ISBN 978-88-6887-042-3

  • D’Elia A (2003) Modelling ranks using the Inverse Hypergeometric distribution. Stat Model 3(1):65–78

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Di Nardo E, Simone R (2019) A model-based fuzzy analysis of questionnaires. Stat Methods App. 28(2):187–215

    Article  MathSciNet  MATH  Google Scholar 

  • Frühwirth-Schnatter S, Gilles C, Robert CP (2019) Handbook of mixture analysis. Handbooks of modern statistical methods, 1st edn. Chapman & Hall, CRC, Boca Raton

    Book  Google Scholar 

  • Grilli L, Iannario M, Piccolo D, Rampichini C (2014) Latent class cub models. Adv Data Anal Classif 8:105–119

    Article  MathSciNet  Google Scholar 

  • Iannario M, Piccolo D (2010) Statistical modelling of subjective survival probabilities. GENUS LXV I(2):17–42

    Google Scholar 

  • Iannario M, Piccolo D (2013) A model-based approach for qualitative assessment in opinion mining. In: Giusti A, Ritter G, Vichi M (eds) Classification and data mining. Springer, Berlin, pp 113–120

    Chapter  Google Scholar 

  • Jacques J, Biernacki C (2018) Model-based co-clustering for ordinal data. Comput Stat Data Anal 123:101–115

    Article  MathSciNet  MATH  Google Scholar 

  • Jolliffe IT, Jolliffe AR (1997) Modelling memory in coal tits. Biometrics 53:1136–1142

    Article  MATH  Google Scholar 

  • Keller K, Sinn M (2007) Ordinal analysis of time series. Phys Ser A 356:114–120

    Google Scholar 

  • Kenett RS, Shmueli G (2014) On information quality. J R Stat Soc Ser A 177(1):3–38

    Article  MathSciNet  Google Scholar 

  • Kenett RS, Shmueli G (2016) Information quality: the potential of data and analytics to generate knowledge. Wiley, Chichester

    Book  Google Scholar 

  • King G, Murray CGL, Salomon JA, Tandon A (2004) Enhancing the validity and cross-cultural comparability of measurement in survey research. Am Polit Sci Rev 98:191–207

    Article  Google Scholar 

  • LeCun Y, Bemgio J, Hinton G (2015) Deep learning. Nature 521:436–444

    Article  Google Scholar 

  • Manisera M, Zuccolotto P (2014) Modeling rating data with nonlinear CUB models. Comput Stat Data Anal 78:100–118

    Article  MathSciNet  MATH  Google Scholar 

  • Manisera M, Zuccolotto P (2015) On the identifiability of nonlinear CUB models. J Multivar Anal 140:302–316

    Article  MATH  Google Scholar 

  • Oberski DL, Vermunt JK (2015) The relationship between CUB and loglinear models with latent variables. Electron J Appl Stat Anal 8(3):374–383

    MathSciNet  Google Scholar 

  • Paccagnella O, Pavan S, Iannario M (2016) Integrating CUB models and Vignette approaches. In: Proceedings SIS 2016 Salerno

  • Piccolo D (2003) On the moments of a mixture of uniform and shifted binomial random variables. Quad Stat 5:85–104

    Google Scholar 

  • Piccolo D (2007) A general approach for modelling individual choices. Quad Stat 9:31–48

    Google Scholar 

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

    Article  Google Scholar 

  • Piccolo D, Simone R (2019) The class of cub models: statistical foundations, inferential issues and empirical evidence. Stat Methods Appl. https://doi.org/10.1007/s10260-019-00461-1

  • Piccolo D, Simone R, Iannario M (2018) Cumulative and CUB models for rating data: a comparative analysis. Int Stat Rev. https://doi.org/10.1111/insr.12282

    Google Scholar 

  • Ridout MS (1999) Memory in coal tits: an alternative models. Biometrics 55:600–662

    Article  MATH  Google Scholar 

  • Simone R (2019) Louis’ identity and fast estimation of mixture models for rating data (under review)

  • Simone R, Capecchi S (2019) A statistical model for voting probabilities. In: Arbia G, Peluso S, Pini A, Rivellilni G (eds) Smart Statistics for Smart Applications, Book of Short Papers SIS2019, Pearson Publisher, Italia, ISBN 9788891915108

  • Simone R, Iannario M (2018) Analysing sport data with clusters of opposite preferences. Stat Model 18(5–6):505–524

    Article  MathSciNet  Google Scholar 

  • Simone R, Tutz G, Iannario M (2019) Subjective heterogeneity in response attitude for multivariate ordinal outcomes. Econom and Stat. https://doi.org/10.1016/j.ecosta.2019.04.002

  • Ursino M (2014) Ordinal data: a new model with applications. Ph.D. Thesis, XXVI cycle, Polytechnic University of Turin, Turin

  • Tutz G, Simone R (2019) Response styles in mixture partial credit models (in preparation)

  • Vermunt JK, Magidson J (2013) Technical guide for Latent GOLD 5.0: basic, advanced, and syntax. Statistical Innovations Inc., Belmont

    Google Scholar 

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Acknowledgements

The research has been partially funded by the ‘cub Regression Model Trees project’ (Project No. 000025_ALTRI_DR_1043_2017-C-CAPPELLI) of the University of Naples Federico II, Italy.

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Correspondence to Rosaria Simone.

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Piccolo, D., Simone, R. Rejoinder to the discussion of “The class of cub models: statistical foundations, inferential issues and empirical evidence”. Stat Methods Appl 28, 477–493 (2019). https://doi.org/10.1007/s10260-019-00479-5

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