Modified generalized method of moments for a robust estimation of polytomous logistic model

1 Center For Clinical And Translational Research, Forsyth Institute, Cambridge, MA, USA
2 Department Of Oral Health Policy And Epidemiology, Harvard School Of Dental Medicine, Cambridge, MA, USA
DOI
10.7287/peerj.preprints.299v1
Published
Accepted
Subject Areas
Epidemiology, Statistics
Keywords
Robust statistics, generalized method of weighted moments, polytomous logistic model
Copyright
© 2014 Wang
Licence
This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Cite this article
Wang X. 2014. Modified generalized method of moments for a robust estimation of polytomous logistic model. PeerJ PrePrints 2:e299v1

Abstract

The maximum likelihood estimation (MLE) method, typically used for polytomous logistic regression, is prone to bias due to both misclassification in outcome and contamination in the design matrix. Hence, robust estimators are needed. In this study, we propose such a method for nominal response data with continuous covariates. A generalized method of weighted moments (GMWM) approach is developed for dealing with contaminated polytomous response data. In this approach, distances are calculated based on individual sample moments. And Huber weights are applied to those observations with large distances. Mellow-type weights are also used to downplay leverage points. We describe theoretical properties of the proposed approach. Simulations suggest that the GMWM performs very well in correcting contamination-caused biases. An empirical application of the GMWM estimator on data from a survet demonstrates its usefulness.