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Robust Inference with Binary Data

Published online by Cambridge University Press:  01 January 2025

Maria-Pia Victoria-Feser
Maria-Pia Victoria-Feser*
Affiliation:
Faculty of Psychology and Educational Sciences, University of Geneva
*
Requests for reprints should be sent to Maxia-Pia Victoria-Feser, HEC, University of Geneva, 40, bd du Pont d' Arve, CH- 1211 Geneva 4, SWITZERLAND.
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Abstract

In this paper robustness properties of the maximum likelihood estimator (MLE) and several robust estimators for the logistic regression model when the responses are binary are analysed. It is found that the MLE and the classical Rao's score test can be misleading in the presence of model misspecification which in the context of logistic regression means either misclassification's errors in the responses, or extreme data points in the design space. A general framework for robust estimation and testing is presented and a robust estimator as well as a robust testing procedure are presented. It is shown that they are less influenced by model misspecifications than their classical counterparts. They are finally applied to the analysis of binary data from a study on breastfeeding.

Keywords

logistic regressionmisclassificationrobust statisticsM-estimatorsRao's score testinfluence functionbreastfeeding
Type
Articles
Information
Psychometrika , Volume 67 , Issue 1 , March 2002 , pp. 21 - 32
Copyright
Copyright © 2002 The Psychometric Society

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Footnotes

The author is partially supported by the Swiss National Science Foundation. She would like to thank Rand Wilcox, Eva Cantoni and Elvezio Ronchetti for their helpful comments on earlier versions of the paper, as well as Stephane Heritier for providing the routine to compute the OBRE.

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