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Score tests for zero-inflation and overdispersion in two-level count data

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  • Lim, Hwa Kyung
  • Song, Juwon
  • Jung, Byoung Cheol

Abstract

In a Poisson regression model in which observations are either clustered or represented by repeated measurements of counts, the number of observed zero counts is sometimes greater than the expected frequency by the Poisson distribution and overdispersion may remain even after modeling excess zeros. The zero-inflated negative binomial (ZINB) mixed regression model is suggested to analyze such data. Previous studies have proposed score statistics for testing zero-inflation and overdispersion separately in correlated count data. Here, we also deal with simultaneous score tests for zero-inflation and overdispersion in two-level count data by using the ZINB mixed regression model. Score tests are suggested for (1) zero-inflation in the presence of overdispersion, (2) overdispersion in the presence of zero-inflation, and (3) zero-inflation and overdispersion simultaneously. The level and power of score test statistics are evaluated by a simulation study. The simulation results indicate that score test statistics may occasionally underestimate or overestimate the nominal significance level due to variation in random effects. This study proposes a parametric bootstrap method to overcome this problem. The simulation results of the bootstrap test indicate that score tests hold the nominal level and provide good power.

Suggested Citation

  • Lim, Hwa Kyung & Song, Juwon & Jung, Byoung Cheol, 2013. "Score tests for zero-inflation and overdispersion in two-level count data," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 67-82.
    • Handle: RePEc:eee:csdana:v:61:y:2013:i:c:p:67-82
    DOI: 10.1016/j.csda.2012.11.006
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Byoung Cheol Jung & Myoungshic Jhun & Jae Won Lee, 2005. "Bootstrap Tests for Overdispersion in a Zero-Inflated Poisson Regression Model," Biometrics, The International Biometric Society, vol. 61(2), pages 626-628, June.
    4. 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.
    5. 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.
    6. 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.
    7. Geert Verbeke & Geert Molenberghs, 2003. "The Use of Score Tests for Inference on Variance Components," Biometrics, The International Biometric Society, vol. 59(2), pages 254-262, June.
    8. 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.
    9. Yang, Zhao & Hardin, James W. & Addy, Cheryl L., 2010. "Score tests for overdispersion in zero-inflated Poisson mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1234-1246, May.
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    Cited by:

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    2. Gul Inan & John Preisser & Kalyan Das, 2018. "A Score Test for Testing a Marginalized Zero-Inflated Poisson Regression Model Against a Marginalized Zero-Inflated Negative Binomial Regression Model," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(1), pages 113-128, March.

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