Qaqish, Bahjat F.; Preisser, John S. Resistant fits for regression with correlated outcomes an estimating equations approach. (English) Zbl 0943.62071 J. Stat. Plann. Inference 75, No. 2, 415-431 (1999). Summary: The generalized estimating equations procedure of K.-Y. Liang and S.L. Zeger [Biometrika 73, 13-22 (1986; Zbl 0595.62110)] can be highly influenced by the presence of unusual data points. A generalization is introduced which yields parameter estimates and fitted values resistant to influential data. A diagonal weight matrix for each cluster is incorporated into the estimating equations which downweights the multivariate response vector element-wise. Efficiency of the procedure is investigated, including the case of correlated binary outcomes. Cited in 5 Documents MSC: 62J20 Diagnostics, and linear inference and regression 62J12 Generalized linear models (logistic models) 62F35 Robustness and adaptive procedures (parametric inference) Keywords:cluster-downweighting; Mallows class; observation-downweighting; Schweppe class; resistant Citations:Zbl 0595.62110 PDFBibTeX XMLCite \textit{B. F. Qaqish} and \textit{J. S. Preisser}, J. Stat. Plann. Inference 75, No. 2, 415--431 (1999; Zbl 0943.62071) Full Text: DOI References: [1] Carroll, R. J.; Pederson, S., On robustness in the logistic regression model, J. R. Statist. Soc. B,, 55, 693-706 (1993) · Zbl 0794.62021 [2] Godambe, Heyde, 1987. Quasi-likelihood and optimal estimation. Int. Statist. Rev. 55, 231-244.; Godambe, Heyde, 1987. Quasi-likelihood and optimal estimation. Int. Statist. Rev. 55, 231-244. · Zbl 0671.62007 [3] Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A., 1986. Robust Statistics: The Approach Based on Influence Functions. Wiley, New York.; Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A., 1986. Robust Statistics: The Approach Based on Influence Functions. Wiley, New York. · Zbl 0593.62027 [4] Holland, P. W.; Welsch, R. E., Robust regression using iteratively reweighted least-squares, Commun. Statist. Theor. Meth., A6, 9, 813-827 (1977) · Zbl 0376.62035 [5] Huggins, R. M., A robust approach to the analysis of repeated measures, Biometrics, 49, 715-720 (1993) [6] Kunsch, H. R.; Stefanski, L. A.; Carroll, R. J., Conditionally unbiased bounded-influence estimation in general regression models, with applications to generalized linear models, J. Amer. Statist. Assoc., 84, 460-466 (1989) · Zbl 0679.62024 [7] Liang, K.-Y.; Zeger, S. L., Longitudinal data analysis using generalized linear models, Biometrika, 73, 13-22 (1986) · Zbl 0595.62110 [8] Mancl, L., Leroux, B., 1996. Efficiency of regression estimates for clustered data. Biometrics 52, 500-511.; Mancl, L., Leroux, B., 1996. Efficiency of regression estimates for clustered data. Biometrics 52, 500-511. · Zbl 0925.62303 [9] McCullagh, P., Nelder, J.A., 1989. Generalized Linear Models, 2nd ed. Chapman & Hall, London.; McCullagh, P., Nelder, J.A., 1989. Generalized Linear Models, 2nd ed. Chapman & Hall, London. · Zbl 0744.62098 [10] Morgenthaler, S., Least-absolute-deviations fits for generalized linear models, Biometrika, 79, 747-754 (1992) · Zbl 0850.62562 [11] Morton, Efficiency of estimating equations and the use of pivots, Biometrika, 68, 227-233 (1981) · Zbl 0469.62023 [12] Preisser, J.; Qaqish, B., Deletion diagnostics for generalized estimating equations, Biometrika, 83, 551-562 (1996) · Zbl 0866.62041 [13] Preisser, J., Qaqish, B., 1999. Robust regression for clustered data with application to binary responses. Biometrics (in press).; Preisser, J., Qaqish, B., 1999. Robust regression for clustered data with application to binary responses. Biometrics (in press). · Zbl 1059.62570 [14] Pregibon, D., Resistant fits for some commonly used logistic models with medical applications, Biometrics, 38, 485-498 (1982) [15] Prentice, R.; Zhao, Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses, Biometrics, 47, 825-839 (1991) · Zbl 0729.62560 [16] Sen, P.K., Singer, J.M., 1985. Large Sample Methods in Statistics. Chapman & Hall, New York.; Sen, P.K., Singer, J.M., 1985. Large Sample Methods in Statistics. Chapman & Hall, New York. [17] Singer, J. M.; Sen, P. K., M-methods in multivariate linear models, J. Multivariate Anal., 17, 168-184 (1985) · Zbl 0579.62026 [18] Williams, D. A., Generalized linear model diagnostics using the deviance and single case deletions, Appl. Statist., 36, 181-191 (1987) · Zbl 0646.62062 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.