Median bias reduction in cumulative link models

This paper presents a novel estimation approach for cumulative link models, based on median bias reduction. The median bias reduced estimator is obtained as solution of an estimating equation based on an adjustment of the score. It allows to obtain higher-order median centering of maximum likelihood estimates without requiring their finiteness. The estimator is equivariant under componentwise monotone reparameterizations and the method is effective in preventing boundary estimates. Through simulation studies and an application, we compare the median bias reduced estimator with the two main competitors, the maximum likelihood and the mean bias reduced estimators. The method is seen to be highly successful in achieving median centering and shows remarkable properties under reparameterizations related to effect measure.