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Some Results on the Log-linear Regression Diagnostics

Yang, Mi-Young;Choi, Ji-Min;Kim, Choong-Rak

  • Published : 2007.08.31

Abstract

In this paper we propose an influence measure for detecting potentially influential observations using the infinitesimal perturbation and the local influence in the log-linear regression model. Also, we propose a goodness-of-fit measure for variable selection. A real data set are used for illustration.

Keywords

Cook's distance;goodness-of-fit;influential perturbations;robust regression

References

  1. Andrews, D. F. and Pregibon, D. (1978). Finding outliers that matter. Journal of the Royal Statistics Society, Ser. B, 40, 85-93
  2. Baker, R. J. and Nelder, J. A. (1978). The GLIM System. Release 3, Generalized Linear Interactive Modelling. Numerical Algorithms Group, Oxford
  3. Belsley, D. A., Kuh, E. and Welsch, R. E. (1980) Regression Diagnostics: Identifying Influential Data and Source of Collinearity. John Wiley & Sons, New York
  4. Cook, R. D. (1986). Assessment of local influence (with discussion). Journal of the Royal Statistical Society, Ser. B, 48, 133-169
  5. Cook, R. D. and Weisberg, S. (1982). Residuals and Influence in Regression. Chapman & Hall/CRC, New York
  6. Fisher, R. A. (1949). A biological assay of tuberculins. Biometrics, 5, 300-316 https://doi.org/10.2307/3001513
  7. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P.J. and Stahel, W. A. (1986). Robust Statistics: The Approach Based on Influence Functions. John Wiley & Sons, New York
  8. Huber, P. J. (1981). Robust Statistics. John Wiley & Sons, New York
  9. Kim, C. (1996). Local influence and replacement measure. Communications in Statistics Theory and Methods, 25, 49-61 https://doi.org/10.1080/03610929608831679
  10. Kim, C. and Storer, B. E. (1996). Reference values for Cook's distance. Communications in Statistics - Simulation and Computation, 25, 691-708 https://doi.org/10.1080/03610919608813337
  11. Maronna, R. A., Martin, D. R. and Yohai, V. J. (2006). Robust Statistics: Theory and Methods. John Wiley & Sons, New York
  12. McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models. 2nd ed., Chapman & Hall/CRC, New York
  13. Pregibon, D. (1981). Logistic regression diagnostics. The Annals of Statistics, 9, 705-724 https://doi.org/10.1214/aos/1176345513
  14. Cook, R. D. (1977). Detection of influential observation in linear regression. Technometrics, 19, 15-18 https://doi.org/10.2307/1268249
  15. Pierce, D. A. and Schafer, D. W. (1986). Residuals in generalized linear models. Journal of the American Statistical Association, 81, 977-986 https://doi.org/10.2307/2289071
  16. Kim, C., Lee, Y. and Park, B-U. (2001). Cook's distance in local polynomial regression. Statistics & Probability Letters, 54, 33-40 https://doi.org/10.1016/S0167-7152(01)00031-1