Median bias reduction in cumulative link models

TL;DR

This paper introduces a median bias reduction method for cumulative link models that improves estimation accuracy, prevents boundary estimates, and is effective in finite samples, outperforming traditional methods.

Contribution

It develops a median bias reduced estimator for cumulative link models based on an adjusted score, offering higher-order median centering and boundary estimate prevention.

Findings

The median bias reduced estimator outperforms maximum likelihood and mean bias reduced estimators in simulations.

The method effectively prevents boundary estimates in cumulative link models.

Application demonstrates solving boundary estimate issues with the proposed estimator.

Abstract

This paper presents a novel estimation approach for cumulative link models, based on median bias reduction as developed in Kenne Pagui et al. (2017). 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. Moreover, the estimator is equivariant under componentwise monotone reparameterizations and the method is effective in preventing boundary estimates. We evaluate the properties of the median bias reduced estimator through simulation studies and compare it with the two main competitors, the maximum likelihood and the mean bias reduced (Firth, 1993) estimators. Finally, we show an application where the proposed estimator is able to solve the boundary estimates problem.