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On testing the hidden heterogeneity in negative binomial regression models

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  • Jeonghwan Kim

    (Inha University)

  • Woojoo Lee

    (Inha University)

Abstract

Negative binomial regression models have been widely used for analyzing overdispersed count data. However, when an important covariate is not included or individuals show some heterogeneity, negative binomial regression models may lead to erroneous standard errors or confidence intervals for the regression parameters. To test the existence of the hidden heterogeneity in negative binomial regression models, score statistics are developed under additive and multiplicative random effect models. We provide the explicit form of the score test statistics and their asymptotic distribution, and investigate the relationship between the score test statistics from the two random effect models. Our numerical study shows that the proposed score statistic has superior performance than existing methods in terms of controlling for the type I error and power.

Suggested Citation

  • Jeonghwan Kim & Woojoo Lee, 2019. "On testing the hidden heterogeneity in negative binomial regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 457-470, May.
    • Handle: RePEc:spr:metrik:v:82:y:2019:i:4:d:10.1007_s00184-018-0684-x
    DOI: 10.1007/s00184-018-0684-x
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    References listed on IDEAS

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    1. N. E. Breslow, 1984. "Extra‐Poisson Variation in Log‐Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(1), pages 38-44, March.
    2. de Jong,Piet & Heller,Gillian Z., 2008. "Generalized Linear Models for Insurance Data," Cambridge Books, Cambridge University Press, number 9780521879149.
    3. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-872, July.
    4. Hinde, John & Demetrio, Clarice G. B., 1998. "Overdispersion: Models and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 27(2), pages 151-170, April.
    5. 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.
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