Open Conference Systems, 50th Scientific meeting of the Italian Statistical Society

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Zero-inflated ordinal data models with application to sport (in)activity
Maria Iannario, Rosaria Simone

Last modified: 2018-05-17


Traditional models for ordinal data (as CUB models or cumulative models with logit/probit link, among others) present limits in explaining the surplus of zero observations, especially when the zeros may relate to two distinct situations of non-participation/inactivity and infrequent participation, for instance. We consider an extension of standard models: zero-inflated CUB models and zero inflated ordered cumulative (ZIOC) probit/logit models handling the GECUB models and usinga double-hurdle combination of a split (logit/probit) model and an ordered probit/logit models, respectively. Both extensions, potentially, relate to different sets of covariates. Finally, models are applied to Sport surveys. Specifically the paper investigates the determinants of sport (in)activity: the frequency and the probabilityof sports participation. It distinguishes between genuine “non-participants†and the ones who do not participate at a time but might under different circumstances.


1. Agresti A.: Analysis of Ordinal Categorical Data, 2nd Ed., J.Wiley & Sons, Hoboken (2010).

2. Barber, N., Havitz, M.E.: Canadian participation rates in ten sport and fitness activities. Journalof Sport Management, 15, 51–76 (2001).

3. Bauman, A., Sallis, J., Dzewaltowski, D., Owen, N.: Toward a better understanding of the influenceson physical activity. American Journal of Preventive Medicine, 23 (2S), 5–14 (2002).

4. Downward, P., Lera-Lòpez, F., Rasciute, S.: The Zero-Inflated ordered probit approach tomodelling sports participation, Economic Modelling, 28, 2469-2477 (2011).

5. Downward, P., Rasciute, S.: The relative demands for sports and leisure in England. EuropeanSport Management Quarterly, 10 (2), 189–214 (2010).

6. Eberth, B., Smith, M.: Modelling the participation decision and duration of sporting activityin Scotland. Economic Modelling, 27 (4), 822–834 (2010).

7. Harris, N.M., Zhao, X.: A zero-inflated ordered probit model, with an application to modellingtobacco consumption. Journal of Econometrics, 141 (2), 1073–1099 (2007).

8. Hovemann, G., Wicker, P.: Determinants of sport participation in the European Union. EuropeanJournal for Sport and Society, 6 (1), 51–59 (2009).

9. Humphreys, B., Ruseski, J.E.: The economic choice of participation and time spent in physicalactivity and sport in Canada, Working Paper No 201014. Department of Economics,University of Alberta (2010).

10. Iannario, M.: Modelling shelter choices in a class of mixture models for ordinal responses.Statistical Methods and Applications, 21, 1–22 (2012).

11. Iannario, M., Piccolo, D.: A generalized framework for modelling ordinal data. StatisticalMethods and Applications, 25, 163–189 (2016).

12. Lera-Lòpez, F., Rapùn-Gàrate, M.: The demand for sport: sport consumption and participationmodels. Journal of Sport Management, 21, 103–122 (2007).

13. Peretti-Watel P., Beck, F., Legleye, S.: Beyond the U-curve: the relationship between sportand alcohol, cigarette and cannabis use in adolescents. Addiction, 97, 707–716 (2002).

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

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