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A goodness-of-fit test for zero-inflated Poisson mixed effects models in tree abundance studies

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  • Liu, Juxin
  • Ma, Yanyuan
  • Johnstone, Jill

Abstract

Field studies in ecology often make use of data collected in a hierarchical fashion, and may combine studies that vary in sampling design. For example, studies of tree recruitment after disturbance may use counts of individual seedlings from plots that vary in spatial arrangement and sampling density. To account for the multi-level design and the fact that more than a few plots usually yield no individuals, a mixed effects zero inflated Poisson model is often adopted. Although it is a convenient modeling strategy, various aspects of the model could be misspecified. A comprehensive test procedure, based on the cumulative sum of the residuals, is proposed. The test is proven to be consistent, and its convergence properties are established as well. The application of the proposed test is illustrated by a real data example and simulation studies.

Suggested Citation

  • Liu, Juxin & Ma, Yanyuan & Johnstone, Jill, 2020. "A goodness-of-fit test for zero-inflated Poisson mixed effects models in tree abundance studies," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:csdana:v:144:y:2020:i:c:s0167947319302427
    DOI: 10.1016/j.csda.2019.106887
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    References listed on IDEAS

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    1. 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.
    2. W. Stute & W. L. Xu & L. X. Zhu, 2008. "Model diagnosis for parametric regression in high-dimensional spaces," Biometrika, Biometrika Trust, vol. 95(2), pages 451-467.
    3. Amemiya, Takeshi, 1981. "Qualitative Response Models: A Survey," Journal of Economic Literature, American Economic Association, vol. 19(4), pages 1483-1536, December.
    4. Tanya P. Garcia & Yanyuan Ma, 2016. "Optimal Estimator for Logistic Model with Distribution-free Random Intercept," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 156-171, March.
    5. Souparno Ghosh & Alan E. Gelfand & Kai Zhu & James S. Clark, 2012. "The k-ZIG: Flexible Modeling for Zero-Inflated Counts," Biometrics, The International Biometric Society, vol. 68(3), pages 878-885, September.
    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.
    7. 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.
    8. D. Y. Lin & L. J. Wei & Z. Ying, 2002. "Model-Checking Techniques Based on Cumulative Residuals," Biometrics, The International Biometric Society, vol. 58(1), pages 1-12, March.
    9. Calama, Rafael & Mutke, Sven & Tomé, José & Gordo, Javier & Montero, Gregorio & Tomé, Margarida, 2011. "Modelling spatial and temporal variability in a zero-inflated variable: The case of stone pine (Pinus pinea L.) cone production," Ecological Modelling, Elsevier, vol. 222(3), pages 606-618.
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