Robustness properties of the ordered logistic discrimination

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 behavior 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 examples. These influence functions may be used to derive diagnostic measures, as will be illustrated on some examples. Furthermore, breakdown points will also be computed