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.
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References
Amemiya T (1984) Tobit models: a survey. J Economet 24: 3–61
Barlow WE, Prentice RL (1988) Residuals for relative risk regression. Biometrika 75: 65–74
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: 316–332
Barros M, Paula GA, Leiva V (2009) An R implementation for generalized Birnbaum-Saunders distributions. Comp Stat Data Anal 53: 1511–1528
Belsley D, Kuh E, Welsch R (1980) Regressions diagnostics: identifying influential data and sources collinearity. Wiley, New York
Chatterjee S, Hadi AS (1988) Sensitivity analysis in linear regression. Wiley, New York
Cohen AC (1991) Truncated and censored samples: theory and applications. Marcel Dekker, New York
Cook RD (1977) Detection of influential observation in linear regression. Technometrics 19: 15–18
Cook RD (1986) Assessment of local influence. J R Stat Soc B 48: 133–169
Cook RD, Weisberg S (1982) Residuals and influence in regression. Chapman and Hall, London
Cook RD, Peña D, Weisberg S (1988) The likelihood displacement: a unifying principle for influence measures. Comm Stat Theor Meth 17: 623–640
Davison A, Gigli A (1989) Deviance residuals and normal scores plots. Biometrika 76: 211–221
Díaz-García JA, Galea M, Leiva V (2003) Influence diagnostics for elliptical multivariate linear regression models. Comm Stat Theor Meth 32: 625–641
Efron B, Hinkley D (1978) Assessing the accuracy of the maximum likelihood estimator: observed vs. expected Fisher information. Biometrika 65: 457–487
Escobar LA, Meeker WQ (1992) Assessing influence in regression analysis with censored data. Biometrika 48: 507–528
Galea M, Paula GA, Bolfarine H (1997) Local influence in elliptical linear regression models. Statistician 46: 71–79
Galea M, Riquelme M, Paula GA (2000) Diagnostics methods in elliptical linear regression models. Braz J Prob Stat 14: 167–184
Galea M, Leiva V, Paula GA (2004) Influence diagnostics in log-Birnbaum-Saunders regression models. J Appl Stat 31: 1049–1064
Klein JP, Moeschberger ML (1997) Survival analysis: techniques for censored and truncated data. Springer, New York
Lawrence AJ (1998) Regression transformation diagnostics using local influence. J Am Stat Soc 84: 125–141
Lee MJ (1995) A semiparametric estimation of simultaneous equations with limited dependent variables: a case study of female labor supply. J Appl Econ 10: 187–200
Lee MJ (1996) Methods of moments and semiparametric econometrics for limited dependent variable models. Springer, New York
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: 5694–5707
Lesaffre E, Verbeke G (1998) Local influence in linear mixed models. Biometrics 54: 570–582
McCullagh P, Nelder JA (1989) Generalized linear models. Chapman and Hall, London
Ortega EM, Bolfarine H, Paula GA (2003) Influence diagnostics in generalized log-gamma regression models. Comp Stat Data Anal 42: 165–186
Osorio F, Paula GA, Galea M (2007) Assessment of local influence in elliptical linear models with longitudinal structure. Comp Stat Data Anal 51: 4354–4368
Paula GA (1993) Assessing local influence in restricted regression models. Comp Stat Data Anal 16: 63–79
Paula GA, Medeiros MJ, Vilca-Labra F (2009) Influence diagnostics for linear models with first autoregressive elliptical errors. Stat Prob Lett 79: 339–346
Poon WY, Poon YS (1999) Conformal normal curvature and assessment of local influence. J R Stat Soc B 61: 51–61
Santos JMC (2001) Influence diagnostics and estimation algorithms for Powell’s SCLS. J Bus Econ Stat 19: 55–62
Schneider H (1986) Truncated and censored samples from normal populations. Marcel Dekker, New York
Scott JL (1997) Regression models of categorical and limited dependent variables. Sage, California
Therneau TM, Grambsch PM, Fleming TR (1990) Martingale-based residuals for survival models. Biometrika 77: 147–160
Tobin J (1958) Estimation of relationships for limited dependent variables. Econometrica 26: 24–36
Xie FC, Wei BC (2007) Diagnostics analysis for log-Birnbaum-Saunders regression models. Comp Stat Data Anal 51: 4692–4706
Zhu H, Zhang H (2004) A diagnostic procedure based on local influence. Biometrika 91: 579–589
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Barros, M., Galea, M., González, M. et al. Influence diagnostics in the tobit censored response model. Stat Methods Appl 19, 379–397 (2010). https://doi.org/10.1007/s10260-010-0135-y
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DOI: https://doi.org/10.1007/s10260-010-0135-y