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Statistical Methods & Applications

, Volume 19, Issue 3, pp 379–397 | Cite as

Influence diagnostics in the tobit censored response model

  • Michelli Barros
  • Manuel Galea
  • Manuel González
  • Víctor Leiva
Article

Abstract

In this article, we develop influence diagnostic tools for the tobit model. Specifically, we discuss global influence methods based on the Cook distance and residuals with envelopes, and total and conformal local influence techniques. In order to analyze the sensitivity of the maximum likelihood estimators of the parameters of the model to small perturbations on the assumptions of the model and/or data, we consider several perturbation schemes, such as case-weight and response perturbations. Finally, we illustrate the developed methodology by means of a real data set.

Keywords

Cook distance Likelihood methods Local influence Residual analysis 

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References

  1. Amemiya T (1984) Tobit models: a survey. J Economet 24: 3–61zbMATHCrossRefMathSciNetGoogle Scholar
  2. Barlow WE, Prentice RL (1988) Residuals for relative risk regression. Biometrika 75: 65–74zbMATHCrossRefMathSciNetGoogle Scholar
  3. Barros M, Paula GA, Leiva V (2008) A new class of survival regression models with heavy-tailed errors: robustness and diagnostics. Lifetime Data Anal 14: 316–332CrossRefMathSciNetGoogle Scholar
  4. Barros M, Paula GA, Leiva V (2009) An R implementation for generalized Birnbaum-Saunders distributions. Comp Stat Data Anal 53: 1511–1528zbMATHCrossRefGoogle Scholar
  5. Belsley D, Kuh E, Welsch R (1980) Regressions diagnostics: identifying influential data and sources collinearity. Wiley, New YorkCrossRefGoogle Scholar
  6. Chatterjee S, Hadi AS (1988) Sensitivity analysis in linear regression. Wiley, New YorkzbMATHCrossRefGoogle Scholar
  7. Cohen AC (1991) Truncated and censored samples: theory and applications. Marcel Dekker, New YorkzbMATHGoogle Scholar
  8. Cook RD (1977) Detection of influential observation in linear regression. Technometrics 19: 15–18zbMATHCrossRefMathSciNetGoogle Scholar
  9. Cook RD (1986) Assessment of local influence. J R Stat Soc B 48: 133–169zbMATHGoogle Scholar
  10. Cook RD, Weisberg S (1982) Residuals and influence in regression. Chapman and Hall, LondonzbMATHGoogle Scholar
  11. Cook RD, Peña D, Weisberg S (1988) The likelihood displacement: a unifying principle for influence measures. Comm Stat Theor Meth 17: 623–640CrossRefGoogle Scholar
  12. Davison A, Gigli A (1989) Deviance residuals and normal scores plots. Biometrika 76: 211–221zbMATHCrossRefGoogle Scholar
  13. Díaz-García JA, Galea M, Leiva V (2003) Influence diagnostics for elliptical multivariate linear regression models. Comm Stat Theor Meth 32: 625–641zbMATHCrossRefGoogle Scholar
  14. Efron B, Hinkley D (1978) Assessing the accuracy of the maximum likelihood estimator: observed vs. expected Fisher information. Biometrika 65: 457–487zbMATHCrossRefMathSciNetGoogle Scholar
  15. Escobar LA, Meeker WQ (1992) Assessing influence in regression analysis with censored data. Biometrika 48: 507–528zbMATHMathSciNetGoogle Scholar
  16. Galea M, Paula GA, Bolfarine H (1997) Local influence in elliptical linear regression models. Statistician 46: 71–79Google Scholar
  17. Galea M, Riquelme M, Paula GA (2000) Diagnostics methods in elliptical linear regression models. Braz J Prob Stat 14: 167–184zbMATHMathSciNetGoogle Scholar
  18. Galea M, Leiva V, Paula GA (2004) Influence diagnostics in log-Birnbaum-Saunders regression models. J Appl Stat 31: 1049–1064zbMATHCrossRefMathSciNetGoogle Scholar
  19. Klein JP, Moeschberger ML (1997) Survival analysis: techniques for censored and truncated data. Springer, New YorkzbMATHGoogle Scholar
  20. Lawrence AJ (1998) Regression transformation diagnostics using local influence. J Am Stat Soc 84: 125–141Google Scholar
  21. Lee MJ (1995) A semiparametric estimation of simultaneous equations with limited dependent variables: a case study of female labor supply. J Appl Econ 10: 187–200CrossRefGoogle Scholar
  22. Lee MJ (1996) Methods of moments and semiparametric econometrics for limited dependent variable models. Springer, New YorkzbMATHGoogle Scholar
  23. Leiva V, Barros M, Paula GA, Galea M (2007) Influence diagnostics in log-Birnbaum-Saunders regression models with censored data. Comp Stat Data Anal 51: 5694–5707zbMATHCrossRefMathSciNetGoogle Scholar
  24. Lesaffre E, Verbeke G (1998) Local influence in linear mixed models. Biometrics 54: 570–582zbMATHCrossRefGoogle Scholar
  25. McCullagh P, Nelder JA (1989) Generalized linear models. Chapman and Hall, LondonzbMATHGoogle Scholar
  26. Ortega EM, Bolfarine H, Paula GA (2003) Influence diagnostics in generalized log-gamma regression models. Comp Stat Data Anal 42: 165–186zbMATHCrossRefMathSciNetGoogle Scholar
  27. Osorio F, Paula GA, Galea M (2007) Assessment of local influence in elliptical linear models with longitudinal structure. Comp Stat Data Anal 51: 4354–4368zbMATHCrossRefMathSciNetGoogle Scholar
  28. Paula GA (1993) Assessing local influence in restricted regression models. Comp Stat Data Anal 16: 63–79zbMATHCrossRefMathSciNetGoogle Scholar
  29. Paula GA, Medeiros MJ, Vilca-Labra F (2009) Influence diagnostics for linear models with first autoregressive elliptical errors. Stat Prob Lett 79: 339–346zbMATHCrossRefGoogle Scholar
  30. Poon WY, Poon YS (1999) Conformal normal curvature and assessment of local influence. J R Stat Soc B 61: 51–61zbMATHCrossRefMathSciNetGoogle Scholar
  31. Santos JMC (2001) Influence diagnostics and estimation algorithms for Powell’s SCLS. J Bus Econ Stat 19: 55–62CrossRefGoogle Scholar
  32. Schneider H (1986) Truncated and censored samples from normal populations. Marcel Dekker, New YorkzbMATHGoogle Scholar
  33. Scott JL (1997) Regression models of categorical and limited dependent variables. Sage, CaliforniaGoogle Scholar
  34. Therneau TM, Grambsch PM, Fleming TR (1990) Martingale-based residuals for survival models. Biometrika 77: 147–160zbMATHCrossRefMathSciNetGoogle Scholar
  35. Tobin J (1958) Estimation of relationships for limited dependent variables. Econometrica 26: 24–36zbMATHCrossRefMathSciNetGoogle Scholar
  36. Xie FC, Wei BC (2007) Diagnostics analysis for log-Birnbaum-Saunders regression models. Comp Stat Data Anal 51: 4692–4706zbMATHCrossRefMathSciNetGoogle Scholar
  37. Zhu H, Zhang H (2004) A diagnostic procedure based on local influence. Biometrika 91: 579–589zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Michelli Barros
    • 1
  • Manuel Galea
    • 2
  • Manuel González
    • 3
  • Víctor Leiva
    • 4
  1. 1.Unidade Acadêmica de Matemática e EstatísticaUniversidade Federal de Campina GrandeParaíbaBrazil
  2. 2.Departamento de EstadísticaPontificia Universidad Católica de ChileSantiagoChile
  3. 3.Empresa El Mercurio SAPSantiagoChile
  4. 4.Departamento de Estadística, CIMFAVUniversidad de ValparaísoValparaísoChile

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