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Three-level zero-inflated Conway–Maxwell–Poisson regression model for analyzing dispersed clustered count data with extra zeros

Author

Listed:
  • Somayeh Ghorbani Gholiabad

    (Hamadan University of Medical Sciences)

  • Abbas Moghimbeigi

    (Alborz University of Medical Sciences)

  • Javad Faradmal

    (Hamadan University of Medical Sciences
    Hamadan University of Medical Sciences)

Abstract

The count response variables are usually included of extra zeros. A useful tool for modeling such data is zero-inflated regression models. In the last decade, the Conway–Maxwell–Poisson model is applied for analyzing count data that can handle under- and over-dispersed data, besides that can encompass the Poisson and negative binomial. Sometimes, due to the sampling design or the data collection procedure, the data simultaneously are clustered or correlated with extra zeros and under- or over-dispersion. We applied a three-level zero-inflated Conway–Maxwell–Poisson regression model to overcome these problems. An expectation-maximization algorithm is used to estimate the model parameters of an appropriate penalized log-likelihood function. Model flexibility and finite-sample properties of this methodology have been investigated by extensive simulation study. The method has been illustrated with an application on real data in the health survey. Furthermore, we compared the results of the model with a three-level zero-inflated negative binomial regression model.

Suggested Citation

  • Somayeh Ghorbani Gholiabad & Abbas Moghimbeigi & Javad Faradmal, 2021. "Three-level zero-inflated Conway–Maxwell–Poisson regression model for analyzing dispersed clustered count data with extra zeros," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 415-439, November.
    • Handle: RePEc:spr:sankhb:v:83:y:2021:i:2:d:10.1007_s13571-020-00229-8
    DOI: 10.1007/s13571-020-00229-8
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    References listed on IDEAS

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    1. Hyoyoung Choo-Wosoba & Somnath Datta, 2018. "Analyzing clustered count data with a cluster-specific random effect zero-inflated Conway–Maxwell–Poisson distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(5), pages 799-814, April.
    2. Royce A. Francis & Srinivas Reddy Geedipally & Seth D. Guikema & Soma Sekhar Dhavala & Dominique Lord & Sarah LaRocca, 2012. "Characterizing the Performance of the Conway‐Maxwell Poisson Generalized Linear Model," Risk Analysis, John Wiley & Sons, vol. 32(1), pages 167-183, January.
    3. Abbas Moghimbeigi & Mohammed Reza Eshraghian & Kazem Mohammad & Brian Mcardle, 2008. "Multilevel zero-inflated negative binomial regression modeling for over-dispersed count data with extra zeros," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1193-1202.
    4. Seth D. Guikema & Jeremy P. Goffelt, 2008. "A Flexible Count Data Regression Model for Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 28(1), pages 213-223, February.
    5. Sellers, Kimberly F. & Raim, Andrew, 2016. "A flexible zero-inflated model to address data dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 68-80.
    6. Moghimbeigi, Abbas & Eshraghian, Mohammad Reza & Mohammad, Kazem & McArdle, Brian, 2009. "A score test for zero-inflation in multilevel count data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1239-1248, February.
    7. Ramesh Gupta & S. Sim & S. Ong, 2014. "Analysis of discrete data by Conway–Maxwell Poisson distribution," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(4), pages 327-343, October.
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