.svg){kind=logo}
ROBUST BINARY LOGISTIC REGRESSION METHODS
Keywords:
maximum likelihood, TLRL estimator, BY estimator, outliers.DOI:
https://doi.org/10.17654/0972361722045Abstract
Binary logistic regression is one of the most popular and widely used models for analyzing the effect of explanatory variables on a binary response variable. The maximum likelihood (ML) method has been generally adopted to estimate the regression parameters. However, the presence of outliers and/or influential observations greatly reduces the accuracy of parameter estimates of ML method. Some robust logistic regression methods such as Bianco-Yohai robust estimator (BY) and Mallows-Huber robust estimator (Mqle) are proposed. These have been programmed in the computer software (R) and used in the presence of outliers. Tabatabai et al. [18] introduced a new robust estimator (TLRL) for binary logistic regression model and a robust estimator for multinomial logistic regression model. In this study, we compare the performance of TLRL estimator with BY and Mqle estimators using a real data set which contain outliers. Additionally, we conduct a simulation study to compare the performances of ML, TLRL, BY and Mqle in the presence of outliers. We identify the outliers using diagnostic graphs and Pearson residuals. A robust version of chi-square statistic is computed to assess the goodness of fit for each model. The results indicate that TLRL method performs similar or better than other methods considered in this study.
Received: April 12, 2022
Accepted: May 30, 2022
References
A. Agresti, An Introduction to Categorical Data Analysis, Wiley, New York, 2007.
O. G. Alema, Comparison of robust regression methods in linear regression, Int. J. Contemp. Math. Sci. 6(9) (2011), 409-421.
T. Bednarski, A note on robust estimation in logistic regression model, Discuss. Math. Probab. Stat. 36 (2016), 43-51.
A. Bergesio and V. J. Yohai, Projection estimators for generalized linear models, J. Amer. Statist. Assoc. 106 (2011), 661-671.
A. M. Bianco and V. J. Yohai, Robust estimation in the logistic regression model in robust statistics, Data Analysis, and Computer Intensive Methods, H. Rieder, ed., Lecture Notes in Statistics, 109, Springer-Verlag, New York, 1996, pp. 17-34.
A. M. Bianco and E. Martinez, Robust testing in the logistic regression model, Comput. Statist. Data Anal. 53 (2009), 4095-4105.
E. Cantoni and E. Ronchetti, Robust inference for generalized linear models, J. Amer. Statist. Assoc. 96 (2001), 1022-1030.
T. Hobza and P. L. Vajda, Robust median estimator in logistic regression, J. Statist. Plann. Inference 138 (2008), 3822-3840.
D. W. Hosmer and S. Lemeshow, Applied Logistic Regression, Wiley, New York, 2000.
N. Kordzakhia, G. D. Mishra and L. Reiersolmoen, Robust estimation in the logistic regression model, J. Statist. Plann. Inference 98 (2001), 211-223.
R. A. Maronna, R. D. Martin and V. J. Yohai, Robust Statistics: Theory and Methods, Wiley, New York, 2006.
E. Marubini and A. Orenti, Pinpointing outliers and influential cases in regression analysis: a robust method at work, Bioinformatics 4(2) (2010), 95-105.
M. A. Merritt et al., Dairy foods and nutrients in relation to risk of ovarian cancer and major histological subtypes, Int. J. Cancer 132(5) (2012), 1114-1124.
C. Mircean et al., Robust estimation of protein expression ratios with lysate microarray technology, Bioinformatics 21(9) (2005), 1935-1942.
J. A. Nelder and R. W. M. Wedderburn, Generalized linear models, J. R. Statist. Soc. A 135 (1972), 370-384.
P. J. Rousseeuw and A. M. Leroy, Robust Regression and Outlier Detection, Wiley, New York, 1987.
M. Tabatabai et al., TELBS robust linear regression method, Open Access Medical Statistics 2 (2012), 65-84.
M. Tabatabai et al., Robust logistic and probit methods for binary and multinomial regression, J. Biomet. Biostat. 5(4) (2014), 202.
D. Timmerman et al., Logistic regression model to distinguish between the benign and malignant adnexal mass before surgery: a multicenter study by the international ovarian tumor analysis group, J. Clinical Oncology 23 (2005), 8794-8801.
V. J. Yohai, High breakdown-point and high efficiency robust estimates for regression, Ann. Statist. 15 (1987), 642-656.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 Pushpa Publishing House, Prayagraj, India
This work is licensed under a Creative Commons Attribution 4.0 International License.
____________________________
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pushpa Publishing House for more info or permissions.
Journal Impact Factor: 
