IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i17p3198-d906462.html
   My bibliography  Save this article

A New Regression Model on the Unit Interval: Properties, Estimation, and Application

Author

Listed:
  • Yury R. Benites

    (Department of Applied Mathematics and Statistics, University of São Paulo, São Carlos 13566-590, Brazil
    These authors contributed equally to this work.)

  • Vicente G. Cancho

    (Department of Applied Mathematics and Statistics, University of São Paulo, São Carlos 13566-590, Brazil
    These authors contributed equally to this work.)

  • Edwin M. M. Ortega

    (Department of Exact Sciences, University of São Paulo, Piracicaba 13418-900, Brazil
    These authors contributed equally to this work.)

  • Roberto Vila

    (Department of Statistics, University of Brasilia, Brasilia 70910-900, Brazil
    These authors contributed equally to this work.)

  • Gauss M. Cordeiro

    (Department of Statistics, Federal University of Pernambuco, Recife 50670-901, Brazil
    These authors contributed equally to this work.)

Abstract

A new and flexible distribution is introduced for modeling proportional data based on the quantile of the generalized extreme value distribution. We obtain explicit expressions for the moments, quantiles, and other structural properties. An extended regression model is constructed as an alternative to compete with the beta regression. Some simulations from the Bayesian perspectives are developed, and an illustrative application to real data involving the comparison of models and influence diagnostics is also addressed.

Suggested Citation

  • Yury R. Benites & Vicente G. Cancho & Edwin M. M. Ortega & Roberto Vila & Gauss M. Cordeiro, 2022. "A New Regression Model on the Unit Interval: Properties, Estimation, and Application," Mathematics, MDPI, vol. 10(17), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3198-:d:906462
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/17/3198/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/17/3198/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Raydonal Ospina & Silvia Ferrari, 2010. "Inflated beta distributions," Statistical Papers, Springer, vol. 51(1), pages 111-126, January.
    2. Ospina, Raydonal & Ferrari, Silvia L.P., 2012. "A general class of zero-or-one inflated beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1609-1623.
    3. Krysicki, Wlodzimierz, 1999. "On some new properties of the beta distribution," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 131-137, April.
    4. Jalmar M.F. Carrasco & Silvia L.P. Ferrari & Reinaldo B. Arellano-Valle, 2014. "Errors-in-variables beta regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(7), pages 1530-1547, July.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lucio Masserini & Matilde Bini & Monica Pratesi, 2017. "Effectiveness of non-selective evaluation test scores for predicting first-year performance in university career: a zero-inflated beta regression approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 693-708, March.
    2. Phillip Li, 2018. "Efficient MCMC estimation of inflated beta regression models," Computational Statistics, Springer, vol. 33(1), pages 127-158, March.
    3. Guillermo Martínez-Flórez & Artur J. Lemonte & Germán Moreno-Arenas & Roger Tovar-Falón, 2022. "The Bivariate Unit-Sinh-Normal Distribution and Its Related Regression Model," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    4. Silvia Noirjean & Mario Biggeri & Laura Forastiere & Fabrizia Mealli & Maria Nannini, 2023. "Estimating causal effects of community health financing via principal stratification," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1317-1350, October.
    5. Ehsan Bahrami Samani & Elham Tabrizi, 2023. "Joint Linear Modeling of Mixed Data and Its Application to Email Analysis," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 175-209, May.
    6. 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.
    7. Murilo Wohlgemuth & Carlos Ernani Fries & Ângelo Márcio Oliveira Sant’Anna & Ricardo Giglio & Diego Castro Fettermann, 2020. "Assessment of the technical efficiency of Brazilian logistic operators using data envelopment analysis and one inflated beta regression," Annals of Operations Research, Springer, vol. 286(1), pages 703-717, March.
    8. Diego Ramos Canterle & Fábio Mariano Bayer, 2019. "Variable dispersion beta regressions with parametric link functions," Statistical Papers, Springer, vol. 60(5), pages 1541-1567, October.
    9. Francisco Cribari-Neto & Sadraque E.F. Lucena, 2015. "Nonnested hypothesis testing in the class of varying dispersion beta regressions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(5), pages 967-985, May.
    10. Guillermo Martínez-Flórez & Roger Tovar-Falón & Carlos Barrera-Causil, 2022. "Inflated Unit-Birnbaum-Saunders Distribution," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    11. Hildete P. Pinheiro & Rafael P. Maia & Eufrásio A. Lima Neto & Mariana Rodrigues-Motta, 2019. "Zero-one augmented beta and zero-inflated discrete models with heterogeneous dispersion for the analysis of student academic performance," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 749-767, December.
    12. Ospina, Raydonal & Ferrari, Silvia L.P., 2012. "A general class of zero-or-one inflated beta regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1609-1623.
    13. Guillermo Martínez-Flórez & Heleno Bolfarine & Héctor Gómez, 2015. "Doubly censored power-normal regression models with inflation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 265-286, June.
    14. Oscar Melo & Carlos Melo & Jorge Mateu, 2015. "Distance-based beta regression for prediction of mutual funds," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(1), pages 83-106, January.
    15. Fábio M. Bayer & Francisco Cribari‐Neto & Jéssica Santos, 2021. "Inflated Kumaraswamy regressions with application to water supply and sanitation in Brazil," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(4), pages 453-481, November.
    16. Luiz M A Lima-Filho & Tarciana Liberal Pereira & Tatiene C Souza & Fábio M Bayer, 2020. "Process monitoring using inflated beta regression control chart," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-20, July.
    17. Guillermo Martínez-Flórez & Hector W. Gomez & Roger Tovar-Falón, 2021. "Modeling Proportion Data with Inflation by Using a Power-Skew-Normal/Logit Mixture Model," Mathematics, MDPI, vol. 9(16), pages 1-20, August.
    18. Becky Tang & Henry A. Frye & Alan E. Gelfand & John A. Silander, 2023. "Zero-Inflated Beta Distribution Regression Modeling," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(1), pages 117-137, March.
    19. Ece Yagman & Malcolm Keswell, 2015. "Accents, Race and Discrimination: Evidence from a Trust Game," SALDRU Working Papers 158, Southern Africa Labour and Development Research Unit, University of Cape Town.
    20. Jorge I. Figueroa-Zúñiga & Cristian L. Bayes & Víctor Leiva & Shuangzhe Liu, 2022. "Robust beta regression modeling with errors-in-variables: a Bayesian approach and numerical applications," Statistical Papers, Springer, vol. 63(3), pages 919-942, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3198-:d:906462. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.