For cumulative link models, we propose a new estimation approach aiming at median bias reduction (Kenne Pagui et al., 2017). Such approach is based on an adjustment of the score function. The method does not require finiteness of the maximum likelihood estimate and is effective in preventing boundary estimates. The resulting estimator is componentwise third-order median unbiased in the continuous case and equivariant under componentwise monotone reparameterizations. Simulation studies and an application compare the proposed method with maximum likelihood and mean bias reduction.
