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An extension of an over-dispersion test for count data

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  • Baksh, M. Fazil
  • Böhning, Dankmar
  • Lerdsuwansri, Rattana

Abstract

While over-dispersion in capture-recapture studies is well known to lead to poor estimation of population size, current diagnostic tools to detect the presence of heterogeneity have not been specifically developed for capture-recapture studies. To address this, a simple and efficient method of testing for over-dispersion in zero-truncated count data is developed and evaluated. The proposed method generalizes an over-dispersion test previously suggested for un-truncated count data and may also be used for testing residual over-dispersion in zero-inflation data. Simulations suggest that the asymptotic distribution of the test statistic is standard normal and that this approximation is also reasonable for small sample sizes. The method is also shown to be more efficient than an existing test for over-dispersion adapted for the capture-recapture setting. Studies with zero-truncated and zero-inflated count data are used to illustrate the test procedures.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:466-474
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    References listed on IDEAS

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    1. Dietz, Ekkehart & Bohning, Dankmar, 2000. "On estimation of the Poisson parameter in zero-modified Poisson models," Computational Statistics & Data Analysis, Elsevier, vol. 34(4), pages 441-459, October.
    2. 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.
    3. Xie, Feng-Chang & Wei, Bo-Cheng & Lin, Jin-Guan, 2009. "Score tests for zero-inflated generalized Poisson mixed regression models," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3478-3489, July.
    4. 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.
    5. 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.
    6. Xie, M. & He, B. & Goh, T. N., 2001. "Zero-inflated Poisson model in statistical process control," Computational Statistics & Data Analysis, Elsevier, vol. 38(2), pages 191-201, December.
    7. Peter G.M. Van Der Heijden & Maarten Cruyff & Hans C. Van Houwelingen, 2003. "Estimating the Size of a Criminal Population from Police Records Using the Truncated Poisson Regression Model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 57(3), pages 289-304, August.
    8. Dankmar Böhning & Dieter Schön, 2005. "Nonparametric maximum likelihood estimation of population size based on the counting distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(4), pages 721-737, August.
    9. 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.
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    Cited by:

    1. Orasa Anan & Dankmar Böhning & Antonello Maruotti, 2017. "Population size estimation and heterogeneity in capture–recapture data: a linear regression estimator based on the Conway–Maxwell–Poisson distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(1), pages 49-79, March.
    2. Mark, Tanya & Lemon, Katherine N. & Vandenbosch, Mark & Bulla, Jan & Maruotti, Antonello, 2013. "Capturing the Evolution of Customer–Firm Relationships: How Customers Become More (or Less) Valuable Over Time," Journal of Retailing, Elsevier, vol. 89(3), pages 231-245.
    3. Dankmar Böhning, 2015. "Power series mixtures and the ratio plot with applications to zero-truncated count distribution modelling," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 201-216, August.

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