Publication: Cressie and Read power-divergences as influence measures for logistic regression models
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2006-07-20
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Elsevier Science BV.
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A sample version of the power-divergence measures of Cressie and Read is proposed for the influence analysis in the logistic regression model. Influence measures are obtained by quantifying the deviation between the sample distribution of an estimate obtained with all the observations and the sample distribution of the same estimate obtained without any observation. In particular, this approach is applied to three estimates of the model: the MLE of regression coefficients vector, the probabilities vector and the linear predictor of a future case. Some examples are considered to clarify the usefulness of the introduced diagnostics.
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Basu, A., Basu, S., 1998. Penalized minimum disparity methods for multinomial models.Statist.Sinica 8,841–860.
Belsley,D.A.,Kuh,E.,Welsch,R.E.,1980. Regression Diagnostics :Identifying Influential Data and Sources of Collinearity. Wiley, NewYork.
Burbea, J., 1984. The Bose–Einstein entropy of degree alpha and its Jensen difference. Utilitas Math. 25, 225–240.
Chen, H.S., Lai, K.,Ying, Z., 2004. Goodness-of-fit tests and minimum power divergence estimators for survival data. Statist. Sinica 14, 231–248.
Cook, R.D., 1986. Assessment of local influence. J. Roy. Statist. Soc., Ser. B 48 (2), 133–169.
Cook,R.D.,Weisberg,S.,1980.Characterization of an empirical influence function for detecting influential cases in regression. Technometrics 22, 495–508.
Cook, R.D.,Weisberg, S., 1982. Residuals and Influence in Regression. Chapman & Hall, London.Cressie, N., Pardo, L., 2000.
Cressie,N.,Pardo,L.,2000.Minimum phi-divergence estimator and hierarchical testing in loglinear models.Statist. Sinica 10, 867–884.
Cressie, N., Pardo, L., 2002. Model checking in loglinear models using phi-divergences and MLEs.J.Statist.Plann. Inference 103, 437–453.
Cressie, N., Read, T.R.C., 1984. Multinomial goodness-of-fit tests. J. Roy. Statist. Soc., Ser. B 46, 440–464.
Cressie, N., Pardo, L., Pardo, M.C., 2003. Size and power considerations for testing loglinear models using phi-divergence test statistics. Statist. Sinica 13, 550–570.
Feigl, P., Zelen, M., 1965. Estimation of exponential probabilities with concomitant information.Biometrics 21, 826–838.
Fokianos, K., 2002. Power divergence family of tests for categorical time series models. Ann. Inst. Statist. Math. 54, 543–564.
Hoaglin, D.C.,Welsch, R.E., 1978. The hat matrix in regression and ANOVA. Amer. Statist. 32, 17–22.
Jiménez-Gamero,M.D.,Muñoz-Pichardo,J.M.,Muñoz-Garcia,J., Pascual-Acosta,A.,2002. Rao distance as a measure of influence in the multivariate linear model.J.Appl.Statist. 29 (6), 841–854.
Johnson,W.,1985.Influence measures for logistic regression: another point of view. Biometrika 72 (1), 59–65.
Kullback, S.,1968.Information Theory and Statistics. Peter Smith, Gloucester, MA.
Lee, A.H., 1988. Assessing partial influence in generalized linear models. Biometrics 44, 71–77.
Lee, A.H., Zhao,Y., 1997. Assessing influence on the goodness of linf in generalized linear models. Statist. Probab. Lett. 31, 351–358.
Muñoz-Pichardo, J.M., Enguix-González, A., Muñoz-García, J., Pascual-Acosta, A., 2004. The Fréchet’s metric as a measures of influence in multivariate linear models with random errors elliptically distributed.Comput. Statist. Data Anal. 46, 469–491.
Pardo,J.A.,Pardo,L.,Pardo,M.C.,2005a.Testing in logistic regression models based on phi-divergences.J.Statist.Plann. Inference, in press.
Pardo, J.A., Pardo, L., Pardo, M.C., 2005b. Minimum phi-divergence estimator in logistic regression models. Statist. Papers, in press.
Pregibon, D., 1982. Logistic regression diagnostics. Ann. Statist. 9, 705–724.
Read, T.R.C., Cressie, N.A.C., 1988. Goodness-of-fit Statistics for Discrete Multivariate Data. Springer,NewYork.
Thomas, W., Cook, R.D., 1989. Assessing influence on regression coefficients in generalized linear models. Biometrika 76 (4), 741–749.
Thomas,W., Cook, R.D., 1990. Assessing influence on predictions from generalized linear models. Technometrics 32 (1), 59–65.
Williams, D.A., 1987. Generalized linear models diagnostics using the deviance and single case deletions. Appl. Statist. 36, 181–191.