  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.
