Abstract
Transformations of covariates are commonly applied in regression analysis. When a parametric transformation family is used, the maximum likelihood estimate of the transformation parameter is often sensitive to minor perturbations of the data. Diagnostics are derived to assess the influence of observations on the covariate transformation parameter in generalized linear models. Three numerical examples are presented to illustrate the usefulness of the proposed diagnostics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Atkinson, A. C. (1986). Diagnostic tests for transformations, Technometrics, 28, 29–38.
Atkinson, A. C. (1988). Transformation unmasked, Technometrics, 30, 311–318.
Box, G. E. P. and Tidwell, P. W. (1962). Transformation of the independent variables, Technometrics, 4, 531–550.
Chatterjee, S. and Hadi, A. S. (1988). Sensitivity Analysis in Linear Regression, Wiley, New York.
Collett, D. (1991). Modelling Binary Data, Chapman and Hall, New York.
Cook, R. D. (1986). Assessment of local influence (with discussion), J. Roy. Statist. Soc. Ser. B, 48, 133–169.
Cook, R. D. (1987). Influence assessment, J. Appl. Statist., 14, 117–131.
Cook, R. D. and Wang, P. C. (1983). Transformations and influential cases in regression, Technometrics, 25, 337–343.
Cook, R. D. and Weisberg, S. (1982). Residuals and Influence in Regression, Chapman and Hall, New York.
Ezekiel, M. and Fox, F. A. (1959). Methods of Correlation and Regression Analysis, Wiley, New York.
Hinkley, D. V. and Wang, S. (1988). More about transformations and influential cases in regression, Technometrics, 30, 435–440.
Lawrance, A. J. (1988). Regression transformation diagnostics using local influence, J. Amer. Statist. Assoc., 83, 1067–1072.
Lee, A. H. (1988). Assessing partial influence in generalized linear models, Biometrics, 44, 71–77.
Ryan, T. A., Joiner, B. L. and Ryan, B. F. (1976). Minilab Student Handbook, Duxbury Press, Boston.
Shih, J. Q. (1993). Regression transformation diagnostics in transform-both-sides model, Statist. Probab. Lett., 16, 411–420.
Thomas, W. and Cook, R. D. (1989). Assessing influence on regression coefficients in generalized linear models, Biometrica, 76, 741–749.
Tsai, C.-L. and Wu, X. (1990). Diagnostics in transformation and weighted regression, Technometrics, 32, 315–322.
Tsai, C.-L. and Wu, X. (1992). Transformation-model diagnostics, Technometrics, 34, 197–202.
Wang, P. C. (1987). Simultaneous transformations and influence in regression, Comm. Statist. Theory Methods, 16, 3417–3425.
Wei, B. C. and Hickernell, F. J. (1996). Regression transformation diagnostics for explanatory variables, Statist. Sinica, 6, 433–454.
Wei, B. C. and Shih, J. Q. (1994a). On statistical models for regression diagnostics, Ann. Inst. Statist. Math., 46, 267–278.
Wei, B. C. and Shih, J. Q. (1994b). Local influence analysis for regression transformation models, Acta Math. Appl. Sinica, 17, 132–143.
Weisberg, S. (1985). Applied Linear Regression, 2nd ed., Wiley, New York.
Wu, X. and Luo, Z. (1993a). Second-order approach to local influence, J. Roy. Statist. Soc. Ser. B, 55, 929–936.
Wu, X. and Luo, Z. (1993b). Residual sum of squares and multiple potential, diagnostics by a second order local approach, Statist. Probab. Lett., 16, 289–296.
Author information
Authors and Affiliations
About this article
Cite this article
Lee, A.H., Yick, J.S. Covariate Transformation Diagnostics for Generalized Linear Models. Annals of the Institute of Statistical Mathematics 51, 383–398 (1999). https://doi.org/10.1023/A:1003874628445
Issue Date:
DOI: https://doi.org/10.1023/A:1003874628445