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Improved estimation in cumulative link models

Kosmidis, I; (2014) Improved estimation in cumulative link models. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY , 76 (1) 169 - 196. 10.1111/rssb.12025. Green and gold open access

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Abstract

For the estimation of cumulative link models for ordinal data, the bias reducing adjusted score equations of Firth in 1993 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 estimator proposed enjoys certain shrinkage properties that are defensible from an experimental point of view relating to the nature of ordinal data.

Type:Article
Title:Improved estimation in cumulative link models
Open access status:An open access publication. A version is also available from UCL Discovery.
DOI:10.1111/rssb.12025
Publisher version:http://dx.doi.org/10.1111/rssb.12025
Additional information:© 2013 The Author. Royal Statistical Society published by John Wiley & Sons Ltd This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. This article was first published online on 3 July 2013, under a subscription licence. This article has since been made Open Access and the licence statement has been updated in this version in June 2014.
Keywords:Adjusted counts, Adjusted score equations, Ordinal response models, Reduction of bias, Shrinkage
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science

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