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Bartlett-corrected tests for varying precision beta regressions with application to environmental biometrics

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  • Ana C Guedes
  • Francisco Cribari-Neto
  • Patrícia L Espinheira

Abstract

Beta regressions are commonly used with responses that assume values in the standard unit interval, such as rates, proportions and concentration indices. Hypothesis testing inferences on the model parameters are typically performed using the likelihood ratio test. It delivers accurate inferences when the sample size is large, but can otherwise lead to unreliable conclusions. It is thus important to develop alternative tests with superior finite sample behavior. We derive the Bartlett correction to the likelihood ratio test under the more general formulation of the beta regression model, i.e. under varying precision. The model contains two submodels, one for the mean response and a separate one for the precision parameter. Our interest lies in performing testing inferences on the parameters that index both submodels. We use three Bartlett-corrected likelihood ratio test statistics that are expected to yield superior performance when the sample size is small. We present Monte Carlo simulation evidence on the finite sample behavior of the Bartlett-corrected tests relative to the standard likelihood ratio test and to two improved tests that are based on an alternative approach. The numerical evidence shows that one of the Bartlett-corrected typically delivers accurate inferences even when the sample is quite small. An empirical application related to behavioral biometrics is presented and discussed.

Suggested Citation

  • Ana C Guedes & Francisco Cribari-Neto & Patrícia L Espinheira, 2021. "Bartlett-corrected tests for varying precision beta regressions with application to environmental biometrics," PLOS ONE, Public Library of Science, vol. 16(6), pages 1-26, June.
  • Handle: RePEc:plo:pone00:0253349
    DOI: 10.1371/journal.pone.0253349
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    References listed on IDEAS

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    1. Chen, Kee Kuo & Chiu, Rong-Her & Chang, Ching-Ter, 2017. "Using beta regression to explore the relationship between service attributes and likelihood of customer retention for the container shipping industry," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 104(C), pages 1-16.
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    Cited by:

    1. Tiago M. Magalhães & Gustavo H. A. Pereira & Denise A. Botter & Mônica C. Sandoval, 2024. "Bartlett corrections for zero-adjusted generalized linear models," Statistical Papers, Springer, vol. 65(4), pages 2191-2209, June.

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