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AStA Advances in Statistical Analysis

, Volume 103, Issue 4, pp 503–526 | Cite as

A new approach to truncated regression for count data

  • Ana María Martínez-RodríguezEmail author
  • Antonio Conde-Sánchez
  • María José Olmo-Jiménez
Original Paper
  • 76 Downloads

Abstract

Standard Poisson and negative binomial truncated regression models for count data include the regressors in the mean of the non-truncated distribution. In this paper, a new approach is proposed so that the explanatory variables determine directly the truncated mean. The main advantage is that the regression coefficients in the new models have a straightforward interpretation as the effect of a change in a covariate on the mean of the response variable. A simulation study has been carried out in order to analyze the performance of the proposed truncated regression models versus the standard ones showing that coefficient estimates are now more accurate in the sense that the standard errors are always lower. Also, the simulation study indicates that the estimates obtained with the standard models are biased. An application to real data illustrates the utility of the introduced truncated models in a hurdle model. Although in the example there are slight differences in the results between the two approaches, the proposed one provides a clear interpretation of the coefficient estimates.

Keywords

Count data Hurdle model Negative binomial regression Poisson regression Truncated models 

Notes

Acknowledgements

We are grateful to the anonymous referees for their careful review and constructive comments that substantially improved the article.

References

  1. Baccini, A., Barabesi, L., Cioni, M., Pisani, C.: Crossing the hurdle: the determinants of individual scientific performance. Scienctometrics 101(3), 2035–2062 (2014)CrossRefGoogle Scholar
  2. Cameron, A.C., Trivedi, P.K.: Regression Analysis of Count Data. Cambridge University Press, New York (2013)CrossRefGoogle Scholar
  3. Chou, Y., Chuang, H.H., Shao, B.B.M.: Information initiatives of mobile retailers: a regression analysis of zero-truncated count data with underdispersion. Appl. Stoch. Models Bus. Ind. 31, 457–463 (2015)MathSciNetCrossRefGoogle Scholar
  4. Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J., Knuth, D.E.: On the Lambert \(W\)-function. Adv. Comput. Math. 5(4), 329–359 (1996)Google Scholar
  5. Fair, R.: A theory of extramarital affairs. J. Polit. Econ. 86, 45–61 (1978)CrossRefGoogle Scholar
  6. Farr, M., Stoeckl, N., Sutton, S.: Recreational fishing and boating: are the determinants the same? Mar. Policy 47, 126–137 (2014)CrossRefGoogle Scholar
  7. Ferrari, S.L.P., Cribari-Nieto, F.: Beta regresssion for modelling rates and proportions. J. Appl. Stat. 31(7), 799–815 (2004)MathSciNetCrossRefGoogle Scholar
  8. Gonzales-Barron, U., Cadavez, V., Butler, F.: Conducting inferential statistics for low microbial counts in foods using the Poisson-gamma regression. Food Control 37, 385–394 (2014)CrossRefGoogle Scholar
  9. Grogger, J.T., Carson, R.T.: Models for truncated counts. J. Appl. Econ. 6, 225–238 (1991)CrossRefGoogle Scholar
  10. Gurmu, S.: Generalized hurdle count data regression models. Econ. Lett. 58, 263–268 (1998)CrossRefGoogle Scholar
  11. Hardin, J.W., Hilbe, J.M.: Regression models for count data from truncated distributions. Stata J. 15, 226–246 (2015)CrossRefGoogle Scholar
  12. Hilbe, J.M.: Negative Binomial Regression. Cambridge University Press, New York (2011)CrossRefGoogle Scholar
  13. Hilbe, J.M.: Modeling Count Data. Cambridge University Press, New York (2014a)CrossRefGoogle Scholar
  14. Hilbe, J.M.: Functions, data and code for count data, R package version 1.3.2. http://CRAN.R-project.org/package=COUNT (2014b)
  15. Jackman, S.: PSCL: Classes and Methods for R Developed in the Political Science Computational Laboratory, Stanford University, R package version 1.4.9. http://CRAN.R-project.org/package=pscl (2015)
  16. Liu, X., Saat, M.R., Qin, X., Barkan, C.P.L.: Analysis of U.S. freight-train derailment severity using zero-truncated negative binomial regression and quantile regression. Accid. Anal. Prev. 5, 87–93 (2013)CrossRefGoogle Scholar
  17. Long, J.S., Freese, J.: Regression Models for Categorical Dependent Variables Using Stata. Stata Press, College Station (2014)zbMATHGoogle Scholar
  18. Martínez-Espiñeira, R., Amoako-Tuffour, J.: Recreation demand analysis under truncation, overdispersion, and endogenous stratification: an application to Gros Morne National Park. J. Environ. Manag. 88, 1320–1332 (2008)CrossRefGoogle Scholar
  19. Mullahy, J.: Specification and testing of some modified count data models. J. Econ. 33, 341–365 (1986)MathSciNetCrossRefGoogle Scholar
  20. O’Neill, M.F., Faddy, M.J.: Use of binary and truncated negative binomial modelling in the analysis of recreational catch data. Fish. Res. 60, 471–477 (2003)CrossRefGoogle Scholar
  21. Pazvakawambwa, L., Indongo, N., Kazembe, L.: A hurdle negative binomial regression model for non-marital fertility in Namibia. J. Math. Syst. Sci. 4, 498–508 (2014)Google Scholar
  22. Prebensen, N.K., Altin, M., Uysal, M.: Length of stay: a case of Northerm Norway. Scand. J. Hosp. Tour. 15(Supplement 1), 28–47 (2015)CrossRefGoogle Scholar
  23. Rigby, R.A., Stasinopoulos, D.M.: Generalized additive models for location, scale and shape. Appl. Stat. 54, 507–554 (2005)MathSciNetzbMATHGoogle Scholar
  24. Santos Silva, J.M.C.: Generalized Poisson regression for positive count data. Commun. Stat. Simul. Comput. 26(3), 1089–1102 (1997)CrossRefGoogle Scholar
  25. Stasinopoulos, D.M., Rigby, R.A.: Generalized additive models for location, scale and shape (GAMLSS) in R. J. Stat. Softw. 23(7), 1–46 (2007)CrossRefGoogle Scholar
  26. Stasinopoulos, D.M., Rigby, R.A.: Generating and fitting truncated (gamlss.family) distributions, R package version 4.3-1, URL http://CRAN.R-project.org/package=gamlss.tr (2015)
  27. Stasinopoulos, D.M., Rigby, R.A.: Generalised Additive Models for Location Scale and Shape, R package version 4.4-0. URL http://CRAN.R-project.org/package=gamlss (2016)
  28. Winkelmann, R.: Econometric Analysis of Count Data. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  29. Yee, T.W: VGAM: Vector Generalized Linear and Additive Models, R package version 1.0-1. http://CRAN.R-project.org/package=VGAM (2016)

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchUniversity of JaénJaénSpain

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