|Reference : Robust ordinal logistic regression|
|Scientific congresses and symposiums : Unpublished conference|
|Physical, chemical, mathematical & earth Sciences : Mathematics|
|Robust ordinal logistic regression|
|Ruwet, Christel [Université de Liège - ULg > Département de mathématique > Statistique mathématique >]|
|Haesbroeck, Gentiane [Université de Liège - ULg > Département de mathématique > Statistique mathématique >]|
|Croux, Christophe [Katholieke Universiteit Leuven - KUL > > ORSTAT Research Center > >]|
|International conference on robust statistics 2010|
|du 28 juin 2010 au 02 juillet 2010|
|[en] Breakdown point ; Diagnostic plot ; Influence function ; Ordinal discrimination ; Maximum likelihood estimator|
|[en] Logistic regression is a widely used tool designed to model the success probability of a Bernoulli random variable depending on some explanatory variables. A generalization of this bimodal model is the multinomial case where the dependent variable has more than two categories. When these categories are naturally ordered (e.g. in questionnaires where individuals are asked whether they strongly disagree, disagree, are indifferent, agree or strongly agree with a given statement), one speaks about ordered or ordinal logistic regression. The classical technique for estimating the unknown parameters is based on Maximum Likelihood estimation.
Maximum Likelihood procedures are however known to be vulnerable to contamination in the data. The lack of robustness of this technique in the simple logistic regression setting has already been investigated in the literature, either by computing breakdown points or influence functions. Robust alternatives have also been constructed for that model. In this talk, the breakdown behaviour of the ML-estimation procedure will be considered in the context of ordinal logistic regression. Influence functions will be computed and shown to be unbounded. A robust alternative based on a weighting idea will then be suggested and illustrated on some
The influence functions of the ordinal logistic regression estimators may be used to
compute classification efficiencies or to derive diagnostic measures, as will be illustrated on some examples.
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