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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
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    Cited by:

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    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.

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