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The gradient test statistic for outlier detection in generalized estimating equations. (English) Zbl 07878506

Summary: We develop diagnostic tools for estimating equations, useful for the analysis of data with longitudinal structure. The gradient statistic introduced by Terrell (2002) is used to propose a case deletion measure, as well as a statistic for the detection of outlying observations using a mean-shift outlier model. The proposed methodology is illustrated with an example.

MSC:

62J20 Diagnostics, and linear inference and regression
62J12 Generalized linear models (logistic models)
62P10 Applications of statistics to biology and medical sciences; meta analysis
62J05 Linear regression; mixed models
Full Text: DOI

References:

[1] Cook, R. D.; Weisberg, S., Residuals and Influence in Regression, 1982, Chapman & Hall: Chapman & Hall New York · Zbl 0564.62054
[2] Enea, M.; Plaia, A., A gradient-based deletion diagnostic measure for generalized linear mixed models, Comm. Statist. Theory Methods, 46, 1972-1982, 2017 · Zbl 1360.62410
[3] Hammill, B. G.; Preisser, J. S., A SAS/IML program for GEE and regression diagnostics, Comput. Statist. Data Anal., 51, 1197-1212, 2006 · Zbl 1157.62466
[4] Jørgensen, B.; Knudsen, S. J., Parameter orthogonality and bias adjustment for estimating functions, Scand. J. Stat., 31, 93-114, 2004 · Zbl 1051.62022
[5] Jung, K., Local influence in generalized estimating equations, Scand. J. Stat., 35, 286-294, 2008 · Zbl 1164.62029
[6] Lemonte, A. J., On the gradient statistic under model misspecification, Statist. Probab. Lett., 380, 390-398, 2013 · Zbl 1489.62067
[7] Lemonte, A. J., The Gradient Test: Another Likelihood-Based Test, 2016, Academic Press: Academic Press London · Zbl 1338.62011
[8] Liang, K.-Y.; Zeger, S. L., Longitudinal data analysis using generalized linear models, Biometrika, 73, 13-22, 1986 · Zbl 0595.62110
[9] Pardo, M. C.; Alonso, R., Influence measures based on the volume of confidence ellipsoids for GEE, Biom. J., 54, 552-567, 2012 · Zbl 1316.62160
[10] Pardo, M. C.; Hobza, T., Outlier detection method in GEEs, Biom. J., 56, 838-850, 2014 · Zbl 1309.62126
[11] Preisser, J. S.; Garcia, D. I., Alternative computational formulae for generalized linear model diagnostics: Identifying influential observations with SAS software, Comput. Statist. Data Anal., 48, 755-764, 2005 · Zbl 1429.62323
[12] Preisser, J. S.; Perin, J., Deletion diagnostics for marginal mean and correlation model parameters in estimating equations, Stat. Comput., 17, 381-393, 2007
[13] Preisser, J. S.; Qaqish, B. F., Deletion diagnostics for generalized estimating equations, Biometrika, 83, 551-562, 1996 · Zbl 0866.62041
[14] Preisser, J. S.; Qaqish, B. F., Robust regression for clustered data with application to binary responses, Biometrics, 55, 574-579, 1999 · Zbl 1059.62570
[15] Preisser, J. S.; Qaqish, B. F.; Perin, J., A note on deletion diagnostics for estimating equations, Biometrika, 95, 509-513, 2008 · Zbl 1437.62584
[16] Qu, A.; Song, P., Assessing robustness of generalised estimating equations and quadratic inference functions, Biometrika, 91, 447-459, 2004 · Zbl 1079.62038
[17] Rotnitzky, A.; Jewell, N. P., Hypothesis testing of regression parameters in semiparametric generalized linear models for clustered data, Biometrika, 77, 485-497, 1990 · Zbl 0734.62075
[18] Terrell, G. R., The gradient statistic, Comput. Sci. Stat., 34, 206-215, 2002
[19] Venezuela, M. K.; Botter, D. A.; Sandoval, M. C., Diagnostic techniques in generalized estimating equations, J. Stat. Comput. Simul., 77, 879-888, 2007 · Zbl 1127.62064
[20] Vens, M.; Ziegler, A., Generalized estimating equations and regression diagnostics for longitudinal controlled clinical trials: A case study, Comput. Statist. Data Anal., 56, 1232-1242, 2012
[21] Wei, W. H.; Fung, W. K., The mean-shift outlier model in general weighted regression and its applications, Comput. Statist. Data Anal., 30, 429-441, 1999 · Zbl 1043.62523
[22] Wei, B. C.; Shih, J. Q., On statistical models for regression diagnostics, Ann. Inst. Statist. Math., 46, 267-278, 1994 · Zbl 0803.62061
[23] Yuan, K. H.; Jennrich, R. I., Asymptotics of estimating equations under natural conditions, J. Multivariate Anal., 65, 245-260, 1998 · Zbl 1126.62329
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