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

TL;DR

This paper develops asymptotic confidence regions and tests for the proportional odds cumulative logit model with monotonicity constraints on ordinal predictors, validated through simulations and applied to school performance data.

Contribution

It introduces a method to perform inference in constrained POCLM, showing asymptotic equivalence of estimators and providing practical confidence regions and tests.

Findings

Asymptotic equivalence of constrained and unconstrained estimators.

Finite sample coverage probabilities are validated via simulation.

Method successfully applied to real school performance data.

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.