Improved estimation in cumulative link models

TL;DR

This paper introduces a bias-reducing estimator for cumulative link models that improves accuracy, maintains invariance properties, and offers practical advantages for analyzing ordinal categorical data.

Contribution

The paper develops a new reduced-bias estimator for cumulative link models using adjusted score equations, enhancing estimation accuracy and practical applicability.

Findings

Reduced-bias estimator has smaller asymptotic bias than MLE.

Estimator respects invariance properties of cumulative link models.

Offers finite, optimal frequentist properties and shrinkage benefits.

Abstract

For the estimation of cumulative link models for ordinal data, the bias-reducing adjusted score equations in \citet{firth:93} are obtained, whose solution ensures an estimator with smaller asymptotic bias than the maximum likelihood estimator. Their form suggests a parameter-dependent adjustment of the multinomial counts, which, in turn suggests the solution of the adjusted score equations through iterated maximum likelihood fits on adjusted counts, greatly facilitating implementation. Like the maximum likelihood estimator, the reduced-bias estimator is found to respect the invariance properties that make cumulative link models a good choice for the analysis of categorical data. Its additional finiteness and optimal frequentist properties, along with the adequate behaviour of related asymptotic inferential procedures make the reduced-bias estimator attractive as a default choice for practical applications. Furthermore, the proposed estimator enjoys certain shrinkage properties that are defensible from an experimental point of view relating to the nature of ordinal data.