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.

翻译：比例优势累积逻辑模型（POCLM）是针对有序响应变量的标准回归模型。通过为对应参数施加单调性约束，可纳入预测变量的有序性。研究表明，基于优化定义的估计量（如最大似然估计）在无约束模型中与在约束模型参数空间内部区域中渐近等价。基于此性质，推导出约束模型的渐近置信域与检验方法，并通过有限样本的简单修正加以改进。通过模拟研究考察了置信域的有限样本覆盖概率。检验内容涵盖单个变量效应、单调性及指定单调性方向。该方法被应用于学校表现评估的实际数据。