Robust logistic regression for ordered and unordered responses

Multinomial regression models and cumulative, adjacent-categories and continuation-ratio models are applied in many fields to analyze unordered or ordered responses with respect to subjects’ profiles. They are typically fitted by maximum likelihood estimators, which unfortunately are sensitive to anomalous data. In order to cope with these data robust M type estimators can be applied. They exploit the properties of the logistic link function and are based on a weighted likelihood approach. The M estimators can be easily implemented numerically, provide reliable inference when data are contaminated and lead to an accurate model specification. Inference based on the M estimators is illustrated in three case studies related to risk attitude in financial investments, diabetes in non-obese adult patients and intensity of chronic pain in aging people.