Rank-preserving regression: a more robust rank regression model against outliers
Mean‐based semi‐parametric regression models such as the popular generalized estimating equations are widely used to improve robustness of inference over parametric models. Unfortunately, such models are quite sensitive to outlying observations. The Wilcoxon‐score‐based rank regression (RR) provides...
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| Published in | Statistics in medicine Vol. 35; no. 19; pp. 3333 - 3346 |
|---|---|
| Main Authors | , , , , , , |
| Format | Journal Article |
| Language | English |
| Published |
England
Blackwell Publishing Ltd
30.08.2016
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0277-6715 1097-0258 1097-0258 |
| DOI | 10.1002/sim.6930 |
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| Abstract | Mean‐based semi‐parametric regression models such as the popular generalized estimating equations are widely used to improve robustness of inference over parametric models. Unfortunately, such models are quite sensitive to outlying observations. The Wilcoxon‐score‐based rank regression (RR) provides more robust estimates over generalized estimating equations against outliers. However, the RR and its extensions do not sufficiently address missing data arising in longitudinal studies. In this paper, we propose a new approach to address outliers under a different framework based on the functional response models. This functional‐response‐model‐based alternative not only addresses limitations of the RR and its extensions for longitudinal data, but, with its rank‐preserving property, even provides more robust estimates than these alternatives. The proposed approach is illustrated with both real and simulated data. Copyright © 2016 John Wiley & Sons, Ltd. |
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| AbstractList | Mean-based semi-parametric regression models such as the popular generalized estimating equations are widely used to improve robustness of inference over parametric models. Unfortunately, such models are quite sensitive to outlying observations. The Wilcoxon-score-based rank regression (RR) provides more robust estimates over generalized estimating equations against outliers. However, the RR and its extensions do not sufficiently address missing data arising in longitudinal studies. In this paper, we propose a new approach to address outliers under a different framework based on the functional response models. This functional-response-model-based alternative not only addresses limitations of the RR and its extensions for longitudinal data, but, with its rank-preserving property, even provides more robust estimates than these alternatives. The proposed approach is illustrated with both real and simulated data. Mean-based semi-parametric regression models such as the popular generalized estimating equations are widely used to improve robustness of inference over parametric models. Unfortunately, such models are quite sensitive to outlying observations. The Wilcoxon-score-based rank regression (RR) provides more robust estimates over generalized estimating equations against outliers. However, the RR and its extensions do not sufficiently address missing data arising in longitudinal studies. In this paper, we propose a new approach to address outliers under a different framework based on the functional response models. This functional-response-model-based alternative not only addresses limitations of the RR and its extensions for longitudinal data, but, with its rank-preserving property, even provides more robust estimates than these alternatives. The proposed approach is illustrated with both real and simulated data. Copyright © 2016 John Wiley & Sons, Ltd. Mean-based semi-parametric regression models such as the popular generalized estimating equations are widely used to improve robustness of inference over parametric models. Unfortunately, such models are quite sensitive to outlying observations. The Wilcoxon-score-based rank regression (RR) provides more robust estimates over generalized estimating equations against outliers. However, the RR and its extensions do not sufficiently address missing data arising in longitudinal studies. In this paper, we propose a new approach to address outliers under a different framework based on the functional response models. This functional-response-model-based alternative not only addresses limitations of the RR and its extensions for longitudinal data, but, with its rank-preserving property, even provides more robust estimates than these alternatives. The proposed approach is illustrated with both real and simulated data. Copyright © 2016 John Wiley & Sons, Ltd.Mean-based semi-parametric regression models such as the popular generalized estimating equations are widely used to improve robustness of inference over parametric models. Unfortunately, such models are quite sensitive to outlying observations. The Wilcoxon-score-based rank regression (RR) provides more robust estimates over generalized estimating equations against outliers. However, the RR and its extensions do not sufficiently address missing data arising in longitudinal studies. In this paper, we propose a new approach to address outliers under a different framework based on the functional response models. This functional-response-model-based alternative not only addresses limitations of the RR and its extensions for longitudinal data, but, with its rank-preserving property, even provides more robust estimates than these alternatives. The proposed approach is illustrated with both real and simulated data. Copyright © 2016 John Wiley & Sons, Ltd. |
| Author | Zhang, Hui Feng, Changyong Tu, Xin M. Kowalski, Jeanne Wu, Pan Chen, Tian Chen, Rui |
| Author_xml | – sequence: 1 givenname: Tian surname: Chen fullname: Chen, Tian email: Correspondence to: Tian Chen, University Hall 2010F, Department of Mathematics and Statistics, University of Toledo, Toledo, OH 43606, U.S.A., tian.chen@utoledo.edu organization: Department of Mathematics and Statistics, University of Toledo, OH, 43606, Toledo, U.S.A – sequence: 2 givenname: Jeanne surname: Kowalski fullname: Kowalski, Jeanne organization: Department of Biostatistics and Bioinformatics, Emory University, GA, 30322, Atlanta, U.S.A – sequence: 3 givenname: Rui surname: Chen fullname: Chen, Rui organization: Consumer Behavior, Amazon.com, Inc. 333 Boren Ave N, WA, 98109, Seattle, U.S.A – sequence: 4 givenname: Pan surname: Wu fullname: Wu, Pan organization: CValue Institute, Christiana Care Health System, John H Ammon Medical Education Center, DE, 19718, Newark, U.S.A – sequence: 5 givenname: Hui surname: Zhang fullname: Zhang, Hui organization: Department of Biostatistics, St. Jude Children's Research Hospital, TN, 38105, Memphis, U.S.A – sequence: 6 givenname: Changyong surname: Feng fullname: Feng, Changyong organization: Department of Biostatistics and Computational Biology, University of Rochester, NY, 14642, Rochester, U.S.A – sequence: 7 givenname: Xin M. surname: Tu fullname: Tu, Xin M. organization: Department of Biostatistics and Computational Biology, University of Rochester, NY, 14642, Rochester, U.S.A |
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| Cites_doi | 10.1080/02664763.2014.925101 10.1002/sim.3853 10.1080/01621459.1996.10476683 10.1002/sim.6026 10.1080/01621459.1999.10473836 10.1002/(SICI)1097-0258(19991130)18:22<3059::AID-SIM247>3.0.CO;2-O 10.1111/j.1467-9868.2011.01020.x 10.1080/01621459.1952.10483446 10.1201/b12123 10.1214/aoms/1177693245 10.1080/02664763.2014.920780 10.1214/aoms/1177692377 10.1080/01621459.1995.10476493 10.1111/j.2517-6161.1994.tb01972.x 10.1002/sim.6560 10.18637/jss.v014.i07 10.1080/03610928308828522 10.1002/sim.5691 10.1093/biomet/90.3.732 10.1093/biomet/93.2.459 10.1080/02331880108802724 10.1002/sim.6199 10.1080/01621459.1990.10475327 10.1161/01.HYP.0000100444.71069.73 10.1016/j.jadohealth.2012.07.005 |
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| Keywords | between-subject attribute linear regression sexual health rank regression semi-parametric regression models |
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| References | Schroeder EB, Liao D, Chambless LE, Prineas RJ, Evans GW, Heiss G. Hypertension, blood pressure, and heart rate variability the atherosclerosis risk in communities (aric) study. Hypertension 2003; 42(6): 1106-1111. Terpstra JT, McKean JW. Rank-based analysis of linear models using r. Journal of Statistical Software 2005; 14(7): 1-26. Jureckova J. Nonparametric estimate of regression coefficients. The Annals of Mathematical Statistics 1971; 42(4): 1328-1338. Jung SH. Quasi-likelihood for median regression models. Journal of the American Statistical Association 1996; 91(433): 251-257. Robins JM, Rotnitzky A, Zhao LP. Analysis of semiparametric regression models for repeated outcomes in the presence of missing data. Journal of the American Statistical Association 1995; 90: 106-121. Van Elteren P. On the Combination of Independent Two Sample Tests of Wilcoxon. Stichting Mathematisch Centrum. Zuivere Wiskunde: Amsterdam, Netherlands, 1959. Chang WH, McKean JW, Naranjo JD, Sheather SJ. High-breakdown rank regression. Journal of the American Statistical Association 1999; 94(445): 205-219. Strauss D, Ikeda M. Pseudolikelihood estimation for social networks. Journal of the American Statistical Association 1990; 85(409): 204-212. Kowalski J, Tu XM. Modern Applied U-statistics, vol. 714. John Wiley & Sons: Hoboken, New Jersey, 2008. Chen R, Chen T, Lu N, Zhang H, Wu P, Feng C, Tu X. Extending the Mann-Whitney-Wilcoxon rank sum test to longitudinal regression analysis. Journal of Applied Statistics 2014; 41(12): 2658-2675. Terpstra JT, McKean JW, Naranjo JD. Highly efficient weighted for autoregression Wilcoxon estimes for autoregression. Statistics: A Journal of Theoretical and Applied Statistics 2000; 35(1): 45-80. Ma Y, Gonzalez Della Valle A, Zhang H, Tu X. A U-statistics-based approach for modeling Cronbach coefficient alpha within a longitudinal data setting. Statistics in Medicine 2010; 29(6): 659-670. Tang W, He H, Tu XM. Applied Categorical and Count Data Analysis. CRC Press: Boca Raton, Florida, 2012. Thas O, Neve JD, Clement L, Ottoy JP. Probabilistic index models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 2012; 74(4): 623-671. Jaeckel LA. Estimating regression coefficients by minimizing the dispersion of the residuals. The Annals of Mathematical Statistics 1972; 43(5): 1449-1458. Wu P, Han Y, Chen T, Tu X. Causal inference for Mann-Whitney-Wilcoxon rank sum and other nonparametric statistics. Statistics in Medicine 2014; 33(8): 1261-1271. Horvitz DG, Thompson DJ. A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association 1952; 47(260): 663-685. Naranjo J, Hettmansperger T. Bounded influence rank regression. Journal of the Royal Statistical Society. Series B (Methodological) 1994; 56(1): 209-220. Sievers GL. A weighted dispersion function for estimation in linear models. Communications in Statistics-Theory and Methods 1983; 12(10): 1161-1179. Yu Q, Chen R, Tang W, He H, Gallop R, Crits-Christoph P, Hu J, Tu X. Distribution-free models for longitudinal count responses with overdispersion and structural zeros. Statistics in Medicine 2013; 32(14): 2390-2405. Tang W, Lu N, Chen T, Wang W, Gunzler DD, Han Y, Tu XM. On performance of parametric and distribution-free models for zero-inflated and over-dispersed count responses. Statistics in Medicine 2015; 34(24): 3235-3245. Jung SH, Ying Z. Rank-based regression with repeated measurements data. Biometrika 2003; 90(3): 732-740. Tu XM, Kowalski J, Jia G. Bayesian analysis of prevalence with covariates using simulation-based techniques: applications to HIV screening. Statistics in Medicine 1999; 18(22): 3059-3073. Wang YG, Zhu M. Rank-based regression for analysis of repeated measures. Biometrika 2006; 93(2): 459-464. Morrison-Beedy D, Jones SH, Xia Y, Tu X, Crean HF, Carey MP. Reducing sexual risk behavior in adolescent girls: results from a randomized controlled trial. Journal of Adolescent Health 2013; 52(3): 314-321. Wu P, Gunzler D, Lu N, Chen T, Wymen P, Tu X. Causal inference for community-based multi-layered intervention study. Statistics in Medicine 2014; 33(22): 3905-3918. Lu N, Chen T, Wu P, Gunzler D, Zhang H, He H, Tu X. Functional response models for intraclass correlation coefficients. 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| References_xml | – reference: Tu XM, Kowalski J, Jia G. Bayesian analysis of prevalence with covariates using simulation-based techniques: applications to HIV screening. Statistics in Medicine 1999; 18(22): 3059-3073. – reference: Ma Y, Gonzalez Della Valle A, Zhang H, Tu X. A U-statistics-based approach for modeling Cronbach coefficient alpha within a longitudinal data setting. Statistics in Medicine 2010; 29(6): 659-670. – reference: Horvitz DG, Thompson DJ. A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association 1952; 47(260): 663-685. – reference: Thas O, Neve JD, Clement L, Ottoy JP. Probabilistic index models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 2012; 74(4): 623-671. – reference: Chen R, Chen T, Lu N, Zhang H, Wu P, Feng C, Tu X. Extending the Mann-Whitney-Wilcoxon rank sum test to longitudinal regression analysis. Journal of Applied Statistics 2014; 41(12): 2658-2675. – reference: Sievers GL. A weighted dispersion function for estimation in linear models. Communications in Statistics-Theory and Methods 1983; 12(10): 1161-1179. – reference: Wu P, Gunzler D, Lu N, Chen T, Wymen P, Tu X. Causal inference for community-based multi-layered intervention study. Statistics in Medicine 2014; 33(22): 3905-3918. – reference: Lu N, Chen T, Wu P, Gunzler D, Zhang H, He H, Tu X. Functional response models for intraclass correlation coefficients. Journal of Applied Statistics 2014; 41(11): 2539-2556. – reference: Schroeder EB, Liao D, Chambless LE, Prineas RJ, Evans GW, Heiss G. Hypertension, blood pressure, and heart rate variability the atherosclerosis risk in communities (aric) study. Hypertension 2003; 42(6): 1106-1111. – reference: Robins JM, Rotnitzky A, Zhao LP. Analysis of semiparametric regression models for repeated outcomes in the presence of missing data. Journal of the American Statistical Association 1995; 90: 106-121. – reference: Van Elteren P. On the Combination of Independent Two Sample Tests of Wilcoxon. Stichting Mathematisch Centrum. Zuivere Wiskunde: Amsterdam, Netherlands, 1959. – reference: Tang W, He H, Tu XM. Applied Categorical and Count Data Analysis. CRC Press: Boca Raton, Florida, 2012. – reference: Tang W, Lu N, Chen T, Wang W, Gunzler DD, Han Y, Tu XM. On performance of parametric and distribution-free models for zero-inflated and over-dispersed count responses. Statistics in Medicine 2015; 34(24): 3235-3245. – reference: Jureckova J. Nonparametric estimate of regression coefficients. The Annals of Mathematical Statistics 1971; 42(4): 1328-1338. – reference: Terpstra JT, McKean JW, Naranjo JD. Highly efficient weighted for autoregression Wilcoxon estimes for autoregression. Statistics: A Journal of Theoretical and Applied Statistics 2000; 35(1): 45-80. – reference: Naranjo J, Hettmansperger T. Bounded influence rank regression. Journal of the Royal Statistical Society. Series B (Methodological) 1994; 56(1): 209-220. – reference: Wu P, Han Y, Chen T, Tu X. Causal inference for Mann-Whitney-Wilcoxon rank sum and other nonparametric statistics. Statistics in Medicine 2014; 33(8): 1261-1271. – reference: Jung SH. Quasi-likelihood for median regression models. Journal of the American Statistical Association 1996; 91(433): 251-257. – reference: Terpstra JT, McKean JW. Rank-based analysis of linear models using r. Journal of Statistical Software 2005; 14(7): 1-26. – reference: Strauss D, Ikeda M. Pseudolikelihood estimation for social networks. Journal of the American Statistical Association 1990; 85(409): 204-212. – reference: Chang WH, McKean JW, Naranjo JD, Sheather SJ. High-breakdown rank regression. Journal of the American Statistical Association 1999; 94(445): 205-219. – reference: Kowalski J, Tu XM. Modern Applied U-statistics, vol. 714. John Wiley & Sons: Hoboken, New Jersey, 2008. – reference: Yu Q, Chen R, Tang W, He H, Gallop R, Crits-Christoph P, Hu J, Tu X. Distribution-free models for longitudinal count responses with overdispersion and structural zeros. Statistics in Medicine 2013; 32(14): 2390-2405. – reference: Jaeckel LA. Estimating regression coefficients by minimizing the dispersion of the residuals. The Annals of Mathematical Statistics 1972; 43(5): 1449-1458. – reference: Morrison-Beedy D, Jones SH, Xia Y, Tu X, Crean HF, Carey MP. Reducing sexual risk behavior in adolescent girls: results from a randomized controlled trial. Journal of Adolescent Health 2013; 52(3): 314-321. – reference: Jung SH, Ying Z. Rank-based regression with repeated measurements data. Biometrika 2003; 90(3): 732-740. – reference: Wang YG, Zhu M. Rank-based regression for analysis of repeated measures. Biometrika 2006; 93(2): 459-464. – volume: 42 start-page: 1328 issue: 4 year: 1971 end-page: 1338 article-title: Nonparametric estimate of regression coefficients publication-title: The Annals of Mathematical Statistics – volume: 93 start-page: 459 issue: 2 year: 2006 end-page: 464 article-title: Rank‐based regression for analysis of repeated measures publication-title: Biometrika – volume: 32 start-page: 2390 issue: 14 year: 2013 end-page: 2405 article-title: Distribution‐free models for longitudinal count responses with overdispersion and structural zeros publication-title: Statistics in Medicine – volume: 90 start-page: 732 issue: 3 year: 2003 end-page: 740 article-title: Rank‐based regression with repeated measurements data publication-title: Biometrika – volume: 56 start-page: 209 issue: 1 year: 1994 end-page: 220 article-title: Bounded influence rank regression publication-title: Journal of the Royal Statistical Society. Series B (Methodological) – volume: 33 start-page: 1261 issue: 8 year: 2014 end-page: 1271 article-title: Causal inference for Mann–Whitney–Wilcoxon rank sum and other nonparametric statistics publication-title: Statistics in Medicine – year: 2003 – volume: 14 start-page: 1 issue: 7 year: 2005 end-page: 26 article-title: Rank‐based analysis of linear models using r publication-title: Journal of Statistical Software – volume: 42 start-page: 1106 issue: 6 year: 2003 end-page: 1111 article-title: Hypertension, blood pressure, and heart rate variability the atherosclerosis risk in communities (aric) study publication-title: Hypertension – volume: 41 start-page: 2539 issue: 11 year: 2014 end-page: 2556 article-title: Functional response models for intraclass correlation coefficients publication-title: Journal of Applied Statistics – volume: 35 start-page: 45 issue: 1 year: 2000 end-page: 80 article-title: Highly efficient weighted for autoregression Wilcoxon estimes for autoregression 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| Snippet | Mean‐based semi‐parametric regression models such as the popular generalized estimating equations are widely used to improve robustness of inference over... Mean-based semi-parametric regression models such as the popular generalized estimating equations are widely used to improve robustness of inference over... |
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| SubjectTerms | between-subject attribute Computer Simulation Data analysis Humans linear regression Longitudinal Studies Mathematical models Models, Statistical Parameter estimation rank regression Regression Analysis semi-parametric regression models sexual health Simulation |
| Title | Rank-preserving regression: a more robust rank regression model against outliers |
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