比例优势累积logit模型在有序预测变量和有序响应变量单调性约束下的推断
Inference for the proportional odds cumulative logit model with monotonicity constraints for ordinal predictors and ordinal response
AI总结：
本文研究有序预测变量和响应变量下比例优势累积logit模型的推断，证明有约束与无约束估计渐近等价，据此构建置信区域和检验，并通过模拟和学校数据验证。
摘要：
比例优势累积logit模型（POCLM）是用于有序响应变量的标准回归模型。预测变量的有序性可以通过对相应参数施加单调性约束来纳入。研究表明，通过优化定义的估计量（如最大似然估计量），对于无约束模型以及位于有约束模型参数空间内部集合中的参数，是渐近等价的。这一性质被用于推导有约束模型的渐近置信区域和检验，并涉及针对有限样本的简单修正。通过模拟研究了置信区域的有限样本覆盖概率。检验涉及单个变量的效应、单调性以及指定的单调性方向。该方法被应用于与学校表现评估相关的真实数据。
英文摘要：
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.
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