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Influence diagnostics in beta regression

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  • Espinheira, Patri­cia L.
  • Ferrari, Silvia L.P.
  • Cribari-Neto, Francisco

Abstract

We consider the issue of assessing influence of observations in the class of beta regression models, which is useful for modelling random variables that assume values in the standard unit interval and are affected by independent variables. We propose a Cook-like distance and also measures of local influence under different perturbation schemes. Applications using real data are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:9:p:4417-4431
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    References listed on IDEAS

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    1. Hongtu Zhu, 2004. "A diagnostic procedure based on local influence," Biometrika, Biometrika Trust, vol. 91(3), pages 579-589, September.
    2. Patricia Espinheira & Silvia Ferrari & Francisco Cribari-Neto, 2008. "On beta regression residuals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(4), pages 407-419.
    3. Paolino, Philip, 2001. "Maximum Likelihood Estimation of Models with Beta-Distributed Dependent Variables," Political Analysis, Cambridge University Press, vol. 9(4), pages 325-346, January.
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    Cited by:

    1. 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.
    2. Artur J. Lemonte & Alexandre G. Patriota, 2011. "Influence diagnostics in Birnbaum--Saunders nonlinear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 871-884, 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. Josephine Gatti Schafer & Caleb T Gallemore, 2016. "Biases in multicriteria decision analysis: The case of environmental planning in Southern Nevada," Environment and Planning C, , vol. 34(8), pages 1652-1675, December.
    5. Lemonte, Artur J., 2013. "A new extended Birnbaum–Saunders regression model for lifetime modeling," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 34-50.
    6. 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.
    7. 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.
    8. Vasconcellos, Klaus L.P. & Zea Fernandez, L.M., 2009. "Influence analysis with homogeneous linear restrictions," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3787-3794, September.
    9. Gueorguieva, Ralitza & Rosenheck, Robert & Zelterman, Daniel, 2008. "Dirichlet component regression and its applications to psychiatric data," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5344-5355, August.
    10. Souza, M.A.O. & Migon, H.S. & Pereira, J.B.M., 2018. "Extended dynamic generalized linear models: The two-parameter exponential family," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 164-179.
    11. Li-Chu Chien, 2011. "Diagnostic plots in beta-regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1607-1622, July.
    12. Zhao, Weihua & Lian, Heng & Zhang, Riquan & Lai, Peng, 2016. "Estimation and variable selection for proportional response data with partially linear single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 40-56.
    13. 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.
    14. Sarah Appiah & Theodore O. Antwi-Asare & F. K. Agyire-Tettey & Emmanuel Abbey & John K. M. Kuwornu & Steven Cole & Sloans K. Chimatiro, 2021. "Livelihood Vulnerabilities Among Women in Small-Scale Fisheries in Ghana," The European Journal of Development Research, Palgrave Macmillan;European Association of Development Research and Training Institutes (EADI), vol. 33(6), pages 1596-1624, December.
    15. Li-Chu Chien & Tsung-Shan Tsou, 2014. "Robust influence diagnostics for generalized linear models with continuous responses," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(4), pages 324-343, November.
    16. Zhao, Weihua & Zhang, Riquan & Huang, Zhensheng & Feng, Jingyan, 2012. "Partially linear single-index beta regression model and score test," Journal of Multivariate Analysis, Elsevier, vol. 103(1), pages 116-123, January.

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