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Regression modeling of one-inflated positive count data

Author

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  • Fatemeh Hassanzadeh

    (University of Isfahan)

  • Iraj Kazemi

    (University of Isfahan)

Abstract

This paper extends regression modeling of positive count data to deal with excessive proportion of one counts. In particular, we propose one-inflated positive (OIP) regression models and present some of their properties. Also, the stochastic hierarchical representation of one-inflated positive poisson and negative binomial regression models are achieved. It is illustrated that the standard OIP model may be inadequate in the presence of one inflation and the lack of independence. Thus, to take into account the inherent correlation of responses, a class of two-level OIP regression models with subjects heterogeneity effects is introduced. A simulation study is conducted to highlight theoretical aspects. Results show that when one-inflation or over-dispersion in the data generating process is ignored, parameter estimates are inefficient and statistically reliable findings are missed. Finally, we analyze a real data set taken from a length of hospital stay study to illustrate the usefulness of our proposed models.

Suggested Citation

  • Fatemeh Hassanzadeh & Iraj Kazemi, 2017. "Regression modeling of one-inflated positive count data," Statistical Papers, Springer, vol. 58(3), pages 791-809, September.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:3:d:10.1007_s00362-015-0726-7
    DOI: 10.1007/s00362-015-0726-7
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    References listed on IDEAS

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    4. Daniel B. Hall, 2000. "Zero-Inflated Poisson and Binomial Regression with Random Effects: A Case Study," Biometrics, The International Biometric Society, vol. 56(4), pages 1030-1039, December.
    5. Lim, Hwa Kyung & Li, Wai Keung & Yu, Philip L.H., 2014. "Zero-inflated Poisson regression mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 151-158.
    6. Rigby, R.A. & Stasinopoulos, D.M. & Akantziliotou, C., 2008. "A framework for modelling overdispersed count data, including the Poisson-shifted generalized inverse Gaussian distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 381-393, December.
    7. Garay, Aldo M. & Hashimoto, Elizabeth M. & Ortega, Edwin M.M. & Lachos, Víctor H., 2011. "On estimation and influence diagnostics for zero-inflated negative binomial regression models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1304-1318, March.
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