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Profile likelihood-based confidence interval for the dispersion parameter in count data

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  • Krishna K. Saha
  • Debaraj Sen
  • Chun Jin

Abstract

The importance of the dispersion parameter in counts occurring in toxicology, biology, clinical medicine, epidemiology, and other similar studies is well known. A couple of procedures for the construction of confidence intervals (CIs) of the dispersion parameter have been investigated, but little attention has been paid to the accuracy of its CIs. In this paper, we introduce the profile likelihood (PL) approach and the hybrid profile variance (HPV) approach for constructing the CIs of the dispersion parameter for counts based on the negative binomial model. The non-parametric bootstrap (NPB) approach based on the maximum likelihood (ML) estimates of the dispersion parameter is also considered. We then compare our proposed approaches with an asymptotic approach based on the ML and the restricted ML (REML) estimates of the dispersion parameter as well as the parametric bootstrap (PB) approach based on the ML estimates of the dispersion parameter. As assessed by Monte Carlo simulations, the PL approach has the best small-sample performance, followed by the REML, HPV, NPB, and PB approaches. Three examples to biological count data are presented.

Suggested Citation

  • Krishna K. Saha & Debaraj Sen & Chun Jin, 2012. "Profile likelihood-based confidence interval for the dispersion parameter in count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(4), pages 765-783, August.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:4:p:765-783
    DOI: 10.1080/02664763.2011.616581
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    References listed on IDEAS

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    1. James O Lloyd-Smith, 2007. "Maximum Likelihood Estimation of the Negative Binomial Dispersion Parameter for Highly Overdispersed Data, with Applications to Infectious Diseases," PLOS ONE, Public Library of Science, vol. 2(2), pages 1-8, February.
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    5. Krishna Saha, 2008. "Semiparametric estimation for the dispersion parameter in the analysis of over- or underdispersed count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(12), pages 1383-1397.
    6. Krishna Saha & Sudhir Paul, 2005. "Bias-Corrected Maximum Likelihood Estimator of the Negative Binomial Dispersion Parameter," Biometrics, The International Biometric Society, vol. 61(1), pages 179-185, March.
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