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

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  • Grün, Bettina
  • Kosmidis, Ioannis
  • Zeileis, Achim

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

  • Grün, Bettina & Kosmidis, Ioannis & Zeileis, Achim, 2012. "Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i11).
    • Handle: RePEc:jss:jstsof:v:048:i11
    DOI: http://hdl.handle.net/10.18637/jss.v048.i11
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    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, November.
    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. Leisch, Friedrich, 2004. "FlexMix: A General Framework for Finite Mixture Models and Latent Class Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i08).
    5. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    6. 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).
    7. Cribari-Neto, Francisco & Zeileis, Achim, 2010. "Beta Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i02).
    8. 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.
    9. Simas, Alexandre B. & Barreto-Souza, Wagner & Rocha, Andréa V., 2010. "Improved estimators for a general class of beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 348-366, February.
    10. 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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    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. Tariq Maqsood & Mark Edwards & Ioanna Ioannou & Ioannis Kosmidis & Tiziana Rossetto & Neil Corby, 2016. "Seismic vulnerability functions for Australian buildings by using GEM empirical vulnerability assessment guidelines," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 80(3), pages 1625-1650, February.
    3. Zhou, Haiming & Huang, Xianzheng, 2022. "Bayesian beta regression for bounded responses with unknown supports," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    4. Emilio Gómez-Déniz & Jorge V Pérez-Rodríguez & José Boza-Chirino, 2020. "Modelling tourist expenditure at origin and destination," Tourism Economics, , vol. 26(3), pages 437-460, May.
    5. 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.
    6. Diederik Strubbe & Laura Jiménez & A. Márcia Barbosa & Amy J. S. Davis & Luc Lens & Carsten Rahbek, 2023. "Mechanistic models project bird invasions with accuracy," Nature Communications, Nature, vol. 14(1), pages 1-15, December.
    7. Cristine Rauber & Francisco Cribari-Neto & Fábio M. Bayer, 2020. "Improved testing inferences for beta regressions with parametric mean link function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 687-717, December.
    8. Di Caterina, Claudia & Kosmidis, Ioannis, 2019. "Location-adjusted Wald statistics for scalar parameters," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 126-142.
    9. Saraev, Vadim & Valatin, Gregory & Peace, Andrew & Quine, Christopher, 2019. "How does a biodiversity value impact upon optimal rotation length? An investigation using species richness and forest stand age," Forest Policy and Economics, Elsevier, vol. 107(C), pages 1-1.
    10. Hui Ye & Anthony Bellotti, 2019. "Modelling Recovery Rates for Non-Performing Loans," Risks, MDPI, vol. 7(1), pages 1-17, February.
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    13. Kearney, Aubrey D. & Wilson, Elisabeth S. & Hollinshead, Dana M. & Poletika, Michael & Kestian, Heather H. & Stigdon, Terry J. & Miller, Eric A. & Fluke, John D., 2023. "Child welfare triage: Use of screening threshold analysis to evaluate intake decision-making," Children and Youth Services Review, Elsevier, vol. 144(C).

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    • 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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