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Boosted Beta Regression

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  • Matthias Schmid
  • Florian Wickler
  • Kelly O Maloney
  • Richard Mitchell
  • Nora Fenske
  • Andreas Mayr

Abstract

: Regression analysis with a bounded outcome is a common problem in applied statistics. Typical examples include regression models for percentage outcomes and the analysis of ratings that are measured on a bounded scale. In this paper, we consider beta regression, which is a generalization of logit models to situations where the response is continuous on the interval (0,1). Consequently, beta regression is a convenient tool for analyzing percentage responses. The classical approach to fit a beta regression model is to use maximum likelihood estimation with subsequent AIC-based variable selection. As an alternative to this established - yet unstable - approach, we propose a new estimation technique called boosted beta regression. With boosted beta regression estimation and variable selection can be carried out simultaneously in a highly efficient way. Additionally, both the mean and the variance of a percentage response can be modeled using flexible nonlinear covariate effects. As a consequence, the new method accounts for common problems such as overdispersion and non-binomial variance structures.

Suggested Citation

  • Matthias Schmid & Florian Wickler & Kelly O Maloney & Richard Mitchell & Nora Fenske & Andreas Mayr, 2013. "Boosted Beta Regression," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-15, April.
    • Handle: RePEc:plo:pone00:0061623
    DOI: 10.1371/journal.pone.0061623
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    References listed on IDEAS

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    2. 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.
    3. Papke, Leslie E & Wooldridge, Jeffrey M, 1996. "Econometric Methods for Fractional Response Variables with an Application to 401(K) Plan Participation Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 619-632, Nov.-Dec..
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    2. Kuangnan Fang & Xinyan Fan & Wei Lan & Bingquan Wang, 2019. "Nonparametric additive beta regression for fractional response with application to body fat data," Annals of Operations Research, Springer, vol. 276(1), pages 331-347, May.
    3. Fabrizio Botti, Marcella Corsi, Giulio Guarini, 2016. "Lo Stato come ‘fornitore’ d’investimenti sociali (State as Social Investments Provider)," Moneta e Credito, Economia civile, vol. 69(273), pages 89-108.
    4. Kim, Jong-Min & Lee, Namgil & Hwang, Sun Young, 2020. "A Copula Nonlinear Granger Causality," Economic Modelling, Elsevier, vol. 88(C), pages 420-430.
    5. Martijn J. Burger & Evert J. Meijers & Marloes M. Hoogerbrugge & Jaume Masip Tresserra, 2015. "Borrowed Size, Agglomeration Shadows and Cultural Amenities in North-West Europe," European Planning Studies, Taylor & Francis Journals, vol. 23(6), pages 1090-1109, June.
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    7. Wladislaw Mill & John Morgan, 2022. "The cost of a divided America: an experimental study into destructive behavior," Experimental Economics, Springer;Economic Science Association, vol. 25(3), pages 974-1001, June.

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