Beta Regression in R
Open accessAbstract
The class of beta regression models is commonly used by practitioners to model variables that assume values in the standard unit interval (0, 1). It is based on the assumption that the dependent variable is beta-distributed and that its mean is related to a set of regressors through a linear predictor with unknown coefficients and a link function. The model also includes a precision parameter which may be constant or depend on a (potentially different) set of regressors through a link function as well. This approach naturally incorporates features such as heteroskedasticity or skewness which are commonly observed in data taking values in the standard unit interval, such as rates or proportions. This paper describes the betareg package which provides the class of beta regressions in the R system for statistical computing. The underlying theory is briefly outlined, the implementation discussed and illustrated in various replication exercises.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Predicted values from OLS models are not bounded above one or below zero, so predicted vote shares for Bryan could be negative or exceed 100 percent.
“In addition, predicted values from OLS models are not bounded above one or below zero, resulting in predicted vote shares for Bryan that could be negative or exceed 100 per cent (Cribari-Neto and Zeileis 2010).”
From Populists at the Polls: Economic Factors in the 1896 Presidential Election (2017) · cites this paper as Cribari-Neto and Zeileis 2010
The Introduction discusses the difficulty of using standard linear regression for responses confined to (0, 1) and describes transforming them before fitting such a model. It does not state that OLS predictions for untransformed shares can fall below zero or exceed one; Bryan vote shares are the citing paper’s application, not an example examined in the source. (LLM, conf=0.72)
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
A Simple Test for Heteroscedasticity and Random Coefficient Variation
Breusch, T. S., & Pagan, A. R. (1979) · Econometrica · doi:10.2307/1911963 · Cited by 5,647 · see citing works
A better lemon squeezer? maximum-likelihood regression with beta-distributed dependent variables.
Smithson, M., & Verkuilen, J. (2006) · Psychological Methods · doi:10.1037/1082-989x.11.1.54 · Cited by 1,788 · see citing works
Flagged first, then by citations
Research works printed but not linked: 20
- Chambers JM, Hastie TJ (eds.) (1992). Statistical Models in S. Chapman & Hall, London.
- Espinheira PL, Ferrari SLP, Cribari-Neto F (2008a). "Influence Diagnostics in Beta Regres- sion." Computational Statistics & Data Analysis, 52(9), 4417-4431.
- Espinheira PL, Ferrari SLP, Cribari-Neto F (2008b). "On Beta Regression Residuals." Journal of Applied Statistics, 35(4), 407-419.
- Ferrari SLP, Cribari-Neto F (2004). "Beta Regression for Modelling Rates and Proportions." Journal of Applied Statistics, 31(7), 799-815.
- Fox J (2002). An R and S-PLUS Companion to Applied Regression. Sage Publications, Thousand Oaks, CA.
- Griffiths WE, Hill RC, Judge GG (1993). Learning and Practicing Econometrics. John Wiley & Sons, New York.
- Kieschnick R, McCullough BD (2003). "Regression Analysis of Variates Observed on (0, 1): Percentages, Proportions and Fractions." Statistical Modelling, 3(3), 193-213.
- Koenker R (1981). "A Note on Studentizing a Test for Heteroscedasticity." Journal of Econo- metrics, 17, 107-112.
- McCullagh P, Nelder JA (1989). Generalized Linear Models. 2nd edition. Chapman & Hall, London.
- Ospina R, Cribari-Neto F, Vasconcellos KLP (2006). "Improved Point and Interval Estimation for a Beta Regression Model." Computational Statistics & Data Analysis, 51(2), 960-981.
- Prater NH (1956). "Estimate Gasoline Yields from Crudes." Petroleum Refiner, 35(5), 236- 238.
- Ramsey JB (1969). "Tests for Specification Error in Classical Linear Least Squares Regression Analysis." Journal of the Royal Statistical Society B, 31, 350-371.
- Simas AB, Barreto-Souza W, Rocha AV (2010). "Improved Estimators for a General Class of Beta Regression Models." Computational Statistics & Data Analysis, 54(2), 348-366.
- Wei BC, Hu YQ, Fung WK (1998). "Generalized Leverage and Its Applications." Scandinavian Journal of Statistics, 25(1), 25-37.
- Zeileis A (2004). "Econometric Computing with HC and HAC Covariance Matrix Estimators." Journal of Statistical Software, 11(10), 1-17. URL http://www.jstatsoft.org/v11/i10/.
- Zeileis A (2006a). "Implementing a Class of Structural Change Tests: An Econometric Com- puting Approach." Computational Statistics & Data Analysis, 50(11), 2987-3008.
- Zeileis A (2006b). "Object-Oriented Computation of Sandwich Estimators." Journal of Sta- tistical Software, 16(9), 1-16. URL http://www.jstatsoft.org/v16/i09/.
- Zeileis A, Hothorn T (2002). "Diagnostic Checking in Regression Relationships." R News, 2(3), 7-10. URL http://CRAN.R-project.org/doc/Rnews/.
- Zeileis A, Kleiber C, Jackman S (2008). "Regression Models for Count Data in R." Journal of Statistical Software, 27(8), 1-25. URL http://www.jstatsoft.org/v27/i08/.
- Zeileis A, Leisch F, Hornik K, Kleiber C (2002). "strucchange: An R Package for Testing for Structural Change in Linear Regression Models." Journal of Statistical Software, 7(2), 1-38. URL http://www.jstatsoft.org/v07/i02/.
Cited by
Sorted by citations
Smajić, S., Prada-Medina, C. A., Landoulsi, Z., Ghelfi, J., Delcambre, S., Dietrich, C., Jarazo, J., Henck, J., Balachandran, S., Pachchek, S., et al. (2022) · Brain · doi:10.1093/brain/awab446 · Cited by 590 · see citing works
A systematic evaluation of single cell RNA-seq analysis pipelines
Vieth, B., Parekh, S., Ziegenhain, C., Enard, W., & Hellmann, I. (2019) · Nature Communications · doi:10.1038/s41467-019-12266-7 · Cited by 265 · see citing works
Uncertainty Displays Using Quantile Dotplots or CDFs Improve Transit Decision-Making
Fernandes, M., Walls, L., Munson, S., Hullman, J., & Kay, M. (2018) · Proceedings of the 2018 CHI Conference on Human Factors in Computing Systems · doi:10.1145/3173574.3173718 · Cited by 175 · see citing works
Working capital management and firms’ profitability: Evidence from emerging Asian countries
Singhania, M., & Mehta, P. (2017) · South Asian Journal of Business Studies · doi:10.1108/sajbs-09-2015-0060 · Cited by 109 · see citing works
Schneider, I., Kugel, H., Redlich, R., Grotegerd, D., Bürger, C., Bürkner, P.-C., Opel, N., Dohm, K., Zaremba, D., Meinert, S., et al. (2018) · Neuropsychopharmacology · doi:10.1038/npp.2017.273 · Cited by 86 · see citing works
Heller, S., White, D., Lee, E., Lawton, J., Pollard, D., Waugh, N., Amiel, S., Barnard, K., Beckwith, A., Brennan, A., et al. (2017) · Health Technology Assessment · doi:10.3310/hta21200 · Cited by 73 · see citing works
Byrd, A. L., Liu, M., Fujimura, K. E., Lyalina, S., Nagarkar, D. R., Charbit, B., Bergstedt, J., Patin, E., Harrison, O. J., Quintana-Murci, L., et al. (2021) · Journal of Experimental Medicine · doi:10.1084/jem.20200606 · Cited by 63 · see citing works
Grubbs, J. B., Lee, B. N., Hoagland, K. C., Kraus, S. W., & Perry, S. L. (2020) · Clinical Psychological Science · doi:10.1177/2167702620922966 · Cited by 63 · see citing works
“Specifically, we fit both a censored regression (i.e., tobit) and a beta regression model using the censReg package for R (Version 0.5-30; Henningsen, 2019) and the betaReg package for R (Version 3.1-2; Cribari-Neto & Zeileis, 2010), respectively.”
MethodInfluentialDevelopmental effects of oxytocin neurons on social affiliation and processing of social information
Nunes, A. R., Gliksberg, M., Varela, S. A. M., Teles, M., Wircer, E., Blechman, J., Petri, G., Levkowitz, G., & Oliveira, R. F. (2021) · The Journal of Neuroscience · doi:10.1523/jneurosci.2939-20.2021 · Cited by 47 · see citing works
Populists at the Polls: Economic Factors in the 1896 Presidential Election
Eichengreen, B., Haines, M., Jaremski, M., & Leblang, D. (2017) · doi:10.3386/w23932 · Cited by 9 · see citing works
- Authors
- Cribari-Neto, F., & Zeileis, A.
- ORCID
- Zeileis, Achim
- Venue
- Journal of Statistical Software
- Publisher
- Foundation for Open Access Statistic
- Published
- 2010
- Volume
- 34
- Issue
- 2
- ISSN
- 1548-7660 (ISSN-L)
- OpenAlex
- W2111940674
- Cited by
- 2,505
- References
- 2
- Citations by year
- 2026: 294 · 2025: 310 · 2024: 237 · 2023: 246 · 2022: 253 · 2021: 254 · 2020: 205 · 2019: 197 · 2018: 131 · 2017: 105 · 2016: 66 · 2015: 57 · 2014: 66 · 2013: 38 · 2012: 31
- FWCI
- 27.33
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- cc-by
- Locations
- Journal of Statistical Software (publishedVersion, cc-by)
- ePubWU Institutional Repository (Wirtschaftsuniversität Wien) (submittedVersion)
- WU Research (submittedVersion, other-oa)
- RePEc: Research Papers in Economics (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- WU Research
- Funders
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Data Analysis with R
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- beta regression, R software, precision parameter, link functions, heteroscedasticity, skewness, rates and proportions
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
