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Score tests for overdispersion in zero-inflated Poisson mixed models

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  • Yang, Zhao
  • Hardin, James W.
  • Addy, Cheryl L.

Abstract

This note is motivated by recent works of Xie et al. (2009) and Xiang et al. (2007). Herein, we simplify the score statistic presented by Xie et al. (2009) to test overdispersion in the zero-inflated generalized Poisson (ZIGP) mixed model, and discuss an extension to test overdispersion in zero-inflated Poisson (ZIP) mixed models. Examples highlight the application of the extended results. The extensive simulation study for testing overdispersion in the Poisson mixed model indicates that the proposed score statistics maintain the nominal level reasonably well. In practice, the appropriate model is chosen based on the approximate mean-variance relationship in the data, and a formal score test based on asymptotic standard normal distribution can be employed for testing overdispersion. A case study is provided to illustrate procedures for data analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:5:p:1234-1246
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    References listed on IDEAS

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    1. 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.
    2. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-872, July.
    3. 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.
    4. Hinde, John & Demetrio, Clarice G. B., 1998. "Overdispersion: Models and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 27(2), pages 151-170, April.
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    Cited by:

    1. 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.
    2. 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.

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