Title: Robust non-ordinal polytomous regression
Authors: Benjamin Poilane - University of Geneva (Switzerland) [presenting]
Julien Miron - University of Geneva (Switzerland)
Eva Cantoni - University of Geneva (Switzerland)
Abstract: Data with non-ordered categorical responses occur in various fields (medicine, sociology, political science). Polytomous regression is a well-used tool to make inference on such data. However, datasets can often contain outlying covariate values or mislabelled responses. In such cases, classical maximum likelihood inference may give disproportionate influence to very few points and thus highly bias the estimation. To counter such effects, one can use robust methods. Existing robust polytomous regression estimators are reviewed, and two new proposals are introduced: a robust GLM-based estimator and the optimal self-standardized B-robust estimator with corresponding Wald-type test statistics. Asymptotic properties of these two methods are derived. Robustness properties and computational costs of the existing and new estimators are compared theoretically and through extensive simulation study. The interest of the methods is illustrated on real datasets.