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

The proportional odds cumulative logit model (POCLM) is a standard regression model for an ordinal response. In this article, ordinality of predictors is incorporated by imposing monotonicity constraints on their corresponding parameters. It is shown that the parameter estimates of an unconstrained model are asymptotically equivalent to the ones of a constrained model when they are in the interior set of the parameter space. This is used in order to derive asymptotic confidence regions and tests for the constrained model based on maximum likelihood estimation, 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.