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Inference for the proportional odds cumulative logit model with monotonicity constraints for ordinal predictors and ordinal response

Javier Espinosa-Brito, Christian Hennig

arXiv 11 Jul 2021 · Econometrics · publishedStatistical Methods & Applications (2025)

arXiv:2107.04946 · PDF · DOI · OpenAlex · Extracted main text

Abstract

The proportional odds cumulative logit model (POCLM) is a standard regression model for an ordinal response. Ordinality of predictors can be incorporated by monotonicity constraints for the corresponding parameters. It is shown that estimators defined by optimization, such as maximum likelihood estimators, for an unconstrained model and for parameters in the interior set of the parameter space of a constrained model are asymptotically equivalent. This is used in order to derive asymptotic confidence regions and tests for the constrained model, involving simple modifications for finite samples. The finite sample coverage probability of the confidence regions is investigated by simulation. Tests concern the effect of individual variables, monotonicity, and a specified monotonicity direction. The methodology is applied on real data related to the assessment of school performance.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
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Showing the top 10 of 35 scored citations.