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Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned

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  • Bettina Gr�n

    ()

  • Ioannis Kosmidis

    ()

  • Achim Zeileis

    ()

Abstract

Beta regression - an increasingly popular approach for modeling rates and proportions - is extended in various directions: (a) bias correction/reduction of the maximum likelihood estimator, (b) beta regression tree models by means of recursive partitioning, (c) latent class beta regression by means of finite mixture models. All three extensions may be of importance for enhancing the beta regression toolbox in practice to provide more reliable inference and capture both observed and unobserved/latent heterogeneity in the data. Using the analogy of Smithson and Verkuilen (2006), these extensions make beta regression not only "a better lemon squeezer" (compared to classical least squares regression) but a full-fledged modern juicer offering lemon-based drinks: shaken and stirred (bias correction and reduction), mixed (finite mixture model), or partitioned (tree model). All three extensions are provided in the R package "betareg" (at least 2.4.0), building on generic algorithms and implementations for bias correction/reduction, model-based recursive partioning, and finite mixture models, respectively. Specifically, the new functions betatree() and betamix() reuse the object-oriented flexible implementation from the R packages "party" and "flexmix", respectively.

Suggested Citation

  • Bettina Gr�n & Ioannis Kosmidis & Achim Zeileis, 2011. "Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned," Working Papers 2011-22, Faculty of Economics and Statistics, University of Innsbruck.
    • Handle: RePEc:inn:wpaper:2011-22
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    References listed on IDEAS

    as
    1. Zeileis, Achim & Leisch, Friedrich & Hornik, Kurt & Kleiber, Christian, 2002. "strucchange: An R Package for Testing for Structural Change in Linear Regression Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 7(i02).
    2. Achim Zeileis & Kurt Hornik, 2007. "Generalized M-fluctuation tests for parameter instability," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(4), pages 488-508.
    3. 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.
    4. Grün, Bettina & Leisch, Friedrich, 2008. "FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i04).
    5. Ospina, Raydonal & Cribari-Neto, Francisco & Vasconcellos, Klaus L.P., 2006. "Improved point and interval estimation for a beta regression model," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 960-981, November.
    6. Zeileis, Achim & Croissant, Yves, 2010. "Extended Model Formulas in R: Multiple Parts and Multiple Responses," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i01).
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    Cited by:

    1. Kathryn M. Irvine & T. J. Rodhouse & Ilai N. Keren, 2016. "Extending Ordinal Regression with a Latent Zero-Augmented Beta Distribution," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(4), pages 619-640, December.
    2. repec:eee:transe:v:104:y:2017:i:c:p:1-16 is not listed on IDEAS

    More about this item

    Keywords

    beta regression; bias correction; bias reduction; recursive partitioning; finite mixture; R;

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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