Extended Beta Regression in R: Shaken, Stirred, Mixed, and Partitioned
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.
|Date of creation:||Oct 2011|
|Date of revision:|
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- 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).
- Achim Zeileis & Yves Croissant, 2010. "Extended Model Formulas in R : Multiple Parts and Multiple Responses," Post-Print hal-01245303, HAL.
- 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.
- 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).
- Zeileis, Achim & Leisch, Friedrich & Hornik, Kurt & Kleiber, Christian, 2001. "Strucchange: An R package for testing for structural change in linear regression models," Technical Reports 2001,26, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
- 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.
- 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.
- 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).
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