IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v75y2021i2p137-160.html
   My bibliography  Save this article

Residual and local influence analyses for unit gamma regressions

Author

Listed:
  • Suelena S. Rocha
  • Patrícia L. Espinheira
  • Francisco Cribari‐Neto

Abstract

We obtain local influence measures and residuals for the unit gamma regression model. In particular, we introduce four residuals that are based on Fisher's iterative scoring parameter estimation algorithm and develop local influence analysis based on several different perturbation schemes: cases weighting, response additive perturbation, and covariate(s) additive perturbation. An empirical application in which variables related to education and investment in research and development are used to explain the proportion of nonpoor people in a set of countries is presented and discussed. Residual and local influence analyses show that the unit gamma regression model yields a good fit to the data, even outperforming the beta regression model. The diagnostic analysis singles out countries whose data are worthy of further investigation. Our results reveal that lower poverty levels are associated with higher shares of investment in high technology. The statistical significance of such a relationship is not sensitive to atypical data points.

Suggested Citation

  • Suelena S. Rocha & Patrícia L. Espinheira & Francisco Cribari‐Neto, 2021. "Residual and local influence analyses for unit gamma regressions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(2), pages 137-160, May.
    • Handle: RePEc:bla:stanee:v:75:y:2021:i:2:p:137-160
    DOI: 10.1111/stan.12229
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/stan.12229
    Download Restriction: no
    File URL: https://libkey.io/10.1111/stan.12229?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Patrícia L. Espinheira & Alisson Oliveira Silva, 2020. "Residual and influence analysis to a general class of simplex regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 523-552, June.
    3. Pablo Mitnik & Sunyoung Baek, 2013. "The Kumaraswamy distribution: median-dispersion re-parameterizations for regression modeling and simulation-based estimation," Statistical Papers, Springer, vol. 54(1), pages 177-192, February.
    4. Silvia L. P. Ferrari & Patricia L. Espinheira & Francisco Cribari‐Neto, 2011. "Diagnostic tools in beta regression with varying dispersion," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(3), pages 337-351, August.
    5. Josmar Mazucheli & André Felipe Berdusco Menezes & Sanku Dey, 2018. "Improved maximum-likelihood estimators for the parameters of the unit-gamma distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(15), pages 3767-3778, August.
    6. 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.
    7. Espinheira, Patri­cia L. & Ferrari, Silvia L.P. & Cribari-Neto, Francisco, 2008. "Influence diagnostics in beta regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4417-4431, May.
    8. Ana C. Guedes & Francisco Cribari-Neto & Patrícia L. Espinheira, 2020. "Modified likelihood ratio tests for unit gamma regressions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(9), pages 1562-1586, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Helton Saulo & Alan Dasilva & Víctor Leiva & Luis Sánchez & Hanns de la Fuente‐Mella, 2022. "Log‐symmetric quantile regression models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(2), pages 124-163, May.
    2. Rodrigo Puentes & Carolina Marchant & Víctor Leiva & Jorge I. Figueroa-Zúñiga & Fabrizio Ruggeri, 2021. "Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model," Mathematics, MDPI, vol. 9(6), pages 1-24, March.

    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. 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.
    2. Pablo Mitnik & Sunyoung Baek, 2013. "The Kumaraswamy distribution: median-dispersion re-parameterizations for regression modeling and simulation-based estimation," Statistical Papers, Springer, vol. 54(1), pages 177-192, February.
    3. 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.
    4. Patrícia L. Espinheira & Alisson Oliveira Silva, 2020. "Residual and influence analysis to a general class of simplex regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 523-552, June.
    5. 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.
    6. Wagner Hugo Bonat & Paulo Justiniano Ribeiro & Walmes Marques Zeviani, 2015. "Likelihood analysis for a class of beta mixed models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(2), pages 252-266, February.
    7. Artur J. Lemonte & Germán Moreno-Arenas, 2020. "On a heavy-tailed parametric quantile regression model for limited range response variables," Computational Statistics, Springer, vol. 35(1), pages 379-398, March.
    8. Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2021. "Autoregressive conditional proportion: A multiplicative-error model for (0,1)-valued time series," MPRA Paper 110954, University Library of Munich, Germany, revised 06 Dec 2021.
    9. 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.
    10. Zhou, Haiming & Huang, Xianzheng, 2022. "Bayesian beta regression for bounded responses with unknown supports," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    11. Weihua Zhao & Riquan Zhang & Yazhao Lv & Jicai Liu, 2014. "Variable selection for varying dispersion beta regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(1), pages 95-108, January.
    12. Mustafa Ç. Korkmaz & Emrah Altun & Morad Alizadeh & M. El-Morshedy, 2021. "The Log Exponential-Power Distribution: Properties, Estimations and Quantile Regression Model," Mathematics, MDPI, vol. 9(21), pages 1-19, October.
    13. 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).
    14. 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.
    15. 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.
    16. Li-Chu Chien, 2013. "Multiple deletion diagnostics in beta regression models," Computational Statistics, Springer, vol. 28(4), pages 1639-1661, August.
    17. 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.
    18. Giovanna Bua & Carmine Trecroci, 2019. "International equity markets interdependence: bigger shocks or contagion in the 21st century?," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 155(1), pages 43-69, February.
    19. 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.
    20. Frank A. La Sorte & Alison Johnston & Toby R. Ault, 2021. "Global trends in the frequency and duration of temperature extremes," Climatic Change, Springer, vol. 166(1), pages 1-14, May.

    More about this item

    Statistics

    Access and download statistics

    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:bla:stanee:v:75:y:2021:i:2:p:137-160. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0039-0402 .

    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.