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:成比例的累积日志模型(POCLM)是常规反应的标准回归模型,预测器的常态性可以通过对相应参数的单一度限制纳入,显示通过优化定义的估测器,如最大概率估测器、未受限制模型和受限制模型参数空间内部参数集参数的测算器,在瞬间等同,用于得出无症状信任区和受限制模型的测试,包括对有限样本进行简单修改;对信任区的有限抽样覆盖概率进行模拟调查;测试涉及个别变量、单度和特定单度方向的影响;该方法用于与评估学校业绩有关的实际数据。