论文标题
贝叶斯非参数序列回归在单调性约束下
Bayesian non-parametric ordinal regression under a monotonicity constraint
论文作者
论文摘要
与标称量表相比，分类结果变量的序数尺度具有对协变量效应的单调性假设的特性。该假设是在常用的比例赔率模型中编码的，但是它与其他参数假设（例如线性和添加性）结合使用。本文中，所考虑的模型是非参数，唯一的条件是协变量对结果类别的影响根据顺序尺度是随机单调的。我们不知道存在适用于推理目的的其他可比多变量模型的存在。我们将先前提出的贝叶斯单调多变量回归模型概括为序数结果，并提出了基于可逆的跳跃马尔可夫链蒙特卡洛的估计程序。该模型基于标记的点过程构建，该过程允许其近似于任意单调回归函数形状，并具有内置的协变量选择属性。我们通过广泛的模拟研究研究了提出方法的性能，并在两个真实的数据示例中证明了其实际应用。
Compared to the nominal scale, the ordinal scale for a categorical outcome variable has the property of making a monotonicity assumption for the covariate effects meaningful. This assumption is encoded in the commonly used proportional odds model, but there it is combined with other parametric assumptions such as linearity and additivity. Herein, the considered models are non-parametric and the only condition imposed is that the effects of the covariates on the outcome categories are stochastically monotone according to the ordinal scale. We are not aware of the existence of other comparable multivariable models that would be suitable for inference purposes. We generalize our previously proposed Bayesian monotonic multivariable regression model to ordinal outcomes, and propose an estimation procedure based on reversible jump Markov chain Monte Carlo. The model is based on a marked point process construction, which allows it to approximate arbitrary monotonic regression function shapes, and has a built-in covariate selection property. We study the performance of the proposed approach through extensive simulation studies, and demonstrate its practical application in two real data examples.
