Skip to main content
Log in

Dealing with heterogeneity in ordinal responses

  • Published:
Quality & Quantity Aims and scope Submit manuscript

Abstract

In sample surveys where people are asked to express their personal opinions it is conceivable to register a high level of indecision among respondents and this circumstance generates sub-optimal statistical analyses caused by large heterogeneity in the responses. In this paper, we discuss a model belonging to the class of generalized cub models which is worthwhile for this kind of surveys. Then, we examine some real case studies where the observed heterogeneity and the subjects’ indecision can be analyzed with the proposed approach leading to convincing interpretations. A comparison with more consolidated models and some concluding remarks end the paper.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • Abela, A.: Solidarity and religion in the European Union: a comparative sociological perspective. In: Xuereb, P. (ed.) The Value(s) of a Constitution for Europe, pp. 71–101. European Documentation and Research Centre, University of Malta, Malta (2004)

    Google Scholar 

  • Agresti, A.: Analysis of Ordinal Categorical Data, 2nd edn. Wiley, Hoboken (2010)

    Book  Google Scholar 

  • Alesina, A., Di Tella, R., MacCulloch, R.: Inequality and happiness: are Europeans and Americans different? J. Public Econ. 88, 2009–2042 (2004)

    Article  Google Scholar 

  • Bailey, K., West, R., Anderson, C.A.: The influence of video games on social, cognitive, and affective information processing. In: Decety, J., Cacioppo, J.T. (eds.) The Oxford Handbook of Social Neuroscience. Oxford University Press, Oxford (2012). doi:10.1093/oxfordhb/9780195342161.013.0066

    Google Scholar 

  • Blanchflower, D., Oswald, A.: Well-being over time in Britain and the USA. J. Public Econ. 88, 1359–1386 (2004)

    Article  Google Scholar 

  • Bruni, L.: Reciprocity, Altruism and the Civil Society. Routledge, London (2008)

    Book  Google Scholar 

  • Corduas, M., Iannario, M., Piccolo, D.: A class of statistical models for evaluating services and performances. In: Bini, M., et al. (eds.) Statistical Methods for the Evaluation of Educational Services and Quality of Products. Contribution to Statistics, pp. 99–117. Physica-Verlag, Berlin (2009)

    Chapter  Google Scholar 

  • Cugnata, F., Salini, S.: Model-based approach for importance-performance analysis. Qual. Quant. 48, 3053–3064 (2014)

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Gadrich, T., Bashkansky, E., Zitickis, R.: Assessing variation: a unifying approach for all scales of measurement. Qual. Quant. 49, 1145–1167 (2015)

    Article  Google Scholar 

  • Gehrlein, W.V., Plassmann, F.: A comparison of theoretical and empirical evaluations of the Borda Compromise. Soc. Choice Welf. 43, 747–772 (2014)

    Article  Google Scholar 

  • Gehrlein, W.V., Lepelley, D., Moyouwou, I.: Voters’ preference diversity, concepts of agreement and Condorcet’s paradox. Qual. Quant. 49, 2345–2368 (2015)

    Article  Google Scholar 

  • Gini, C.: Variabilità e mutabilità. Studi economico-giuridici, Facoltà di Giurisprudenza, Universitàdi Cagliari, A, III, parte II (1912)

  • Greene, W.H.: Some Accounting for Excess Zeros and Sample Selection in Poisson and Negative Binomial Regression Models. Working Paper EC-94-10, Department of Economics, New York University (1994)

  • Grofman, B., Uhlaner, C.: Metapreferences and reasons for stability in social choice: thoughts on broadening and clarifying the debate. Theory Decis. 19, 31–50 (1985)

    Article  Google Scholar 

  • Guttman, L.: A basis for scaling qualitative data. Am. Soc. Rev. 9, 139–150 (1944)

    Article  Google Scholar 

  • Hall, D.B.: Zero-inflated poisson and binomial regression with random effects: a case study. Biometrics 56, 1030–1039 (2000)

    Article  Google Scholar 

  • Iannario, M.: Modelling shelter choices in a class of mixture models for ordinal responses. Stat. Methods Appl. 21, 1–22 (2012)

    Article  Google Scholar 

  • Iannario, M., Piccolo, D.: CUB models: statistical methods and empirical evidence. In: Kenett, R.S., Salini, S. (eds.) Modern Analysis of Customer Surveys: With Applications Using R, pp. 231–258. Wiley, Chichester (2012a)

    Google Scholar 

  • Iannario, M., Piccolo, D.: A framework for modelling ordinal data in rating surveys. In: Proceedings of Joint Statistical Meetings, Section on Statistics in Marketing. San Diego, California, pp. 3308–3322 (2012b)

  • Iannario, M., Piccolo, D., Simone, R.: CUB: A class of mixture models for ordinal data. R package version 0.1. http://CRAN.R-project.org/package=CUB (2015)

  • Kakvani, N., Khandker, S., Son, H.H.: Pro-poor growth: concepts and measurement with country case studies. International Poverty Center Working Paper, 2004-1, Brasil (2007)

  • Kankaras, M., Moors, G.: Heterogeneity in solidarity attitudes in Europe. Insights from a multiple-group latentclass factor approach. IRISS Working Papers, 2007-06 (2007)

  • Laakso, M., Taagepera, R.: Effective number of parties: a measure with application to West Europe. Comp. Polit. Stud. 12, 3–27 (1989)

    Article  Google Scholar 

  • Lambert, D.: Zero-inflated poisson regression, with an application to defects in manufacturing. Technometrics 34, 1–14 (1992)

    Article  Google Scholar 

  • Lloyd, C.J.: Statistical Analysis of Categorical Data. Wiley, New York (1999)

    Google Scholar 

  • Manisera, M., Zuccolotto, P.: Modelling “Don’t know” responses in rating scales. Pattern Recogn. Lett. 45, 226–234 (2014b)

    Article  Google Scholar 

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

    Google Scholar 

  • McCullagh, P., Nelder, J.A.: Generalized Linear Models, 2nd edn. Chapman & Hall, London (1989)

    Book  Google Scholar 

  • Molenberghs, G., Verbeke, G.: Likelihood ratio, score, and Wald tests in a constrained parameter space. Am. Stat. 61, 22–27 (2007)

    Article  Google Scholar 

  • Moors, G.: Facts and artifacts in the comparison of attitudes among ethnic minorities. A multigroup latent class structure model with adjustment for response style behavior. Eur. Sociol. Rev. 20, 303–320 (2004)

    Article  Google Scholar 

  • Moors, G.: Exploring the effect of a middle response category on response style in attitude measurement. Qual. Quant. 42, 779–794 (2008)

    Article  Google Scholar 

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

    Google Scholar 

  • Ravallion, M.: Pro-poor growth: a primer. Policy Research Working Paper, WPS3242, March. World Bank, Washington DC. (2004)

  • Stevens, S.S.: On the theory of scales of measurement. Science 103, 677–680 (1946)

    Article  Google Scholar 

  • Self, S.G., Liang, K.Y.: Asymptotic properties of maximum likelihood estimators and likelihood ratio test under nonstandard conditions. J. Am. Stat. Assoc. 82, 605–610 (2003)

    Article  Google Scholar 

  • Trezzini, B.: A measure of multidimensional polarization for categorical diversity data. Qual. Quant. 47, 313–333 (2013)

    Article  Google Scholar 

  • Tutz, G.: Regression for Categorical Data. Cambridge University Press, Cambridge (2012)

    Google Scholar 

  • Vu, H.T.V., Zhou, S.: Generalization of likelihood ratio tests under nonstandard conditions. Ann Stat. 25, 897–916 (1997)

    Article  Google Scholar 

  • Wu, H.-H., Shieh, J.-I.: Quantifying uncertainty in applying importance-performance analysis. Qual. Quant. 44, 997–1003 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Domenico Piccolo.

Additional information

This work has been partially supported by FIRB2012 project at University of Perugia (code RBFR12SHVV) and the frame of Programme STAR (CUP E68C13000020003) at University of Naples Federico II, financially supported by UniNA and Compagnia di San Paolo.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Capecchi, S., Piccolo, D. Dealing with heterogeneity in ordinal responses. Qual Quant 51, 2375–2393 (2017). https://doi.org/10.1007/s11135-016-0393-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11135-016-0393-3

Keywords

Navigation