Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Local Influence of the Quasi-likelihood Estimators in Generalized Linear Models

  • Jung, Kang-Mo (Department of Information Statistics, Kunsan National University)
  • Published : 2007.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

We present a diagnostic method for the quasi-likelihood estimators in generalized linear models. Since these estimators can be usually obtained by iteratively reweighted least squares which are well known to be very sensitive to unusual data, a diagnostic step is indispensable to analysis of data. We extend the local influence approach based on the maximum likelihood function to that on the quasi-likelihood function. Under several perturbation schemes local influence diagnostics are derived. An illustrative example is given and we compare the results provided by local influence and deletion.

Keywords

References

  1. Allison, T. and Cicchetti, D. (1976). Sleep in mammals: Ecological and constitutional correlates. Science, 194, 732-734 https://doi.org/10.1126/science.982039
  2. Cook, R. D. (1986). Assessment of local influence. Journal of the Royal Statistical Society, Ser. B, 48, 133-169
  3. Davis, C. S. (2002). Statistical Methods for the Analysis of Repeated Measurements, Springer-Verlag, New York
  4. Dobson, A. J. (2002). An Introduction to Generalized Linear Models. 2nd ed., Chapman & Hall/CRC
  5. Emerson, J. D., Hoaglin, D. C. and Kempthorne, P. J. (1984). Leverage in least squares additive-plus-multiplicative fits for two-way tables. Journal of the American Statistical Association, 79, 329-335 https://doi.org/10.2307/2288272
  6. Faraway, J. J. (2006). Extending the Linear Model with R. Chapman & Hall/CRC
  7. Lesaffre, E. and Verbeke, G. (1998). Local influence in linear mixed models. Biometrics, 54, 570-582 https://doi.org/10.2307/3109764
  8. McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models. 2nd ed., Chapman & Hall/CRC
  9. Nelder, J. A. and Wedderburn, R. W. M. (1972). Generalized linear models, Journal of the Royal Statistical Society, A, 135, 370-384 https://doi.org/10.2307/2344614
  10. Suarez Rancel, M. M. and Gonzalez Sierra, M. A. (2001). Regression diagnostic using local influence: a review. Communications in Statistics - Theory and Methods, 30, 799-813 https://doi.org/10.1081/STA-100002258
  11. Thomas, W. and Cook, R. D. (1989). Assessing influence on regression coefficients in generalized linear models. Biometrika, 76, 741-749 https://doi.org/10.1093/biomet/76.4.741
  12. Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika, 61, 439-447
  13. Zhu, H. and Zhang, H. (2004). A diagnostic procedure based on local influence, Biometrika, 91, 579-589 https://doi.org/10.1093/biomet/91.3.579