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Multilevel zero-inflated negative binomial regression modeling for over-dispersed count data with extra zeros

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  • Abbas Moghimbeigi
  • Mohammed Reza Eshraghian
  • Kazem Mohammad
  • Brian Mcardle

Abstract

Count data with excess zeros often occurs in areas such as public health, epidemiology, psychology, sociology, engineering, and agriculture. Zero-inflated Poisson (ZIP) regression and zero-inflated negative binomial (ZINB) regression are useful for modeling such data, but because of hierarchical study design or the data collection procedure, zero-inflation and correlation may occur simultaneously. To overcome these challenges ZIP or ZINB may still be used. In this paper, multilevel ZINB regression is used to overcome these problems. The method of parameter estimation is an expectation-maximization algorithm in conjunction with the penalized likelihood and restricted maximum likelihood estimates for variance components. Alternative modeling strategies, namely the ZIP distribution are also considered. An application of the proposed model is shown on decayed, missing, and filled teeth of children aged 12 years old.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:35:y:2008:i:10:p:1193-1202
    DOI: 10.1080/02664760802273203
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    References listed on IDEAS

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    1. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    2. 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.
    3. Jansakul, N. & Hinde, J. P., 2002. "Score Tests for Zero-Inflated Poisson Models," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 75-96, July.
    4. D. Böhning & E. Dietz & P. Schlattmann & L. Mendonça & U. Kirchner, 1999. "The zero‐inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(2), pages 195-209.
    5. William H. Greene, 1994. "Accounting for Excess Zeros and Sample Selection in Poisson and Negative Binomial Regression Models," Working Papers 94-10, New York University, Leonard N. Stern School of Business, Department of Economics.
    6. Martin Ridout & John Hinde & Clarice G. B. Demétrio, 2001. "A Score Test for Testing a Zero‐Inflated Poisson Regression Model Against Zero‐Inflated Negative Binomial Alternatives," Biometrics, The International Biometric Society, vol. 57(1), pages 219-223, March.
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    Cited by:

    1. Kong, Maiying & Xu, Sheng & Levy, Steven M. & Datta, Somnath, 2015. "GEE type inference for clustered zero-inflated negative binomial regression with application to dental caries," Computational Statistics & Data Analysis, Elsevier, vol. 85(C), pages 54-66.
    2. Baksh, M. Fazil & Böhning, Dankmar & Lerdsuwansri, Rattana, 2011. "An extension of an over-dispersion test for count data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 466-474, January.
    3. 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.
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    6. Young Bae & Byung-Deuk Woo & Sungwon Jung & Eunchae Lee & Jiin Lee & Mingu Lee & Haegyun Park, 2023. "The Relationship Between Government Response Speed and Sentiments of Public Complaints: Empirical Evidence From Big Data on Public Complaints in South Korea," SAGE Open, , vol. 13(2), pages 21582440231, April.
    7. 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.
    8. Jun Yang & Min Xie & Thong Ngee Goh, 2011. "Outlier identification and robust parameter estimation in a zero-inflated Poisson model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(2), pages 421-430, October.

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