Ordinal outcome data with covariates occur frequently in statistical practice including applications from biomedicine to marketing research. Most existing methods for this type of data have relied on subjectively specified models that allow order restriction. There are also some semiparametric ordinal models which are more flexible than parametric ones, with fixed link function, they are still not flexible enough to capture the true link or the relationship between the response and covariates. We propose a broadly applicable robust semiparametric ordinal regression model, in which the relationship between the response and covariates is modelled with a nonparametric monotone increasing link function and parametric regression coefficients. This model is more robust and flexible than existing semiparametric and parametric models for this problem. The semiparametric maximum likelihood estimate is used to estimate the model parameters, and the asymptotic properties of the estimates are derived. Simulation studies show clear advantages of the proposed model over existing parametric models, and a real data analysis illustrates the utility of the proposed method.

中文翻译：

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序数响应的鲁棒回归模型

具有协变量的序数结果数据在统计实践中经常出现，包括从生物医学到市场研究的应用。用于此类数据的大多数现有方法都依赖于主观指定的模型，该模型允许进行订单限制。还有一些半参数序数模型比参数半数序数模型更灵活，具有固定链接功能，它们仍然不够灵活，无法捕获真实的链接或响应与协变量之间的关系。我们提出了一种广泛适用的鲁棒半参数有序回归模型，其中，响应和协变量之间的关系是使用非参数单调递增链接函数和参数回归系数建模的。对于该问题，此模型比现有的半参数和参数模型更健壮和灵活。使用半参数最大似然估计来估计模型参数，并得出估计的渐近性质。仿真研究表明，与现有的参数模型相比，该模型具有明显的优势，而实际数据分析表明了该方法的实用性。