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Beta Regression for Modelling Rates and Proportions

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  • Silvia Ferrari
  • Francisco Cribari-Neto

Abstract

This paper proposes a regression model where the response is beta distributed using a parameterization of the beta law that is indexed by mean and dispersion parameters. The proposed model is useful for situations where the variable of interest is continuous and restricted to the interval (0, 1) and is related to other variables through a regression structure. The regression parameters of the beta regression model are interpretable in terms of the mean of the response and, when the logit link is used, of an odds ratio, unlike the parameters of a linear regression that employs a transformed response. Estimation is performed by maximum likelihood. We provide closed-form expressions for the score function, for Fisher's information matrix and its inverse. Hypothesis testing is performed using approximations obtained from the asymptotic normality of the maximum likelihood estimator. Some diagnostic measures are introduced. Finally, practical applications that employ real data are presented and discussed.

Suggested Citation

  • Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
  • Handle: RePEc:taf:japsta:v:31:y:2004:i:7:p:799-815 DOI: 10.1080/0266476042000214501
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    References listed on IDEAS

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    1. G. Robin Henderson, 2001. "EWMA and industrial applications to feedback adjustment and control," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(3-4), pages 399-407.
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