This study proposes an interpretable neural network-based non-proportional odds model (N3POM) for ordinal regression. In the model, the response variable can take continuous values, and the regression coefficients vary depending on the predicting ordinal response. Contrary to conventional approaches, where the linear coefficients of regression are directly estimated from the discrete response, we train a non-linear neural network that outputs the linear coefficients by taking the response as its input. By virtue of the neural network, N3POM may have flexibility while preserving the interpretability of the conventional ordinal regression. We show a sufficient condition under which the predicted conditional cumulative probability (CCP) locally satisfies the monotonicity constraint over a user-specified region in the covariate space. We also provide a monotonicity-preserving stochastic (MPS) algorithm for adequately training the neural network.

翻译：本研究提出一种可解释的基于神经网络的非比例优势模型（N3POM），用于有序回归分析。在该模型中，响应变量可取连续值，且回归系数随预测的有序响应而变化。不同于传统方法直接从离散响应中估计线性回归系数，我们训练一个以响应为输入的非线性神经网络，由其输出线性系数。借助神经网络，N3POM在保持传统有序回归可解释性的同时具备灵活性。我们给出了一个充分条件，使得预测的条件累积概率（CCP）在协变量空间中用户指定区域内局部满足单调性约束。此外，我们还提出了一种保持单调性的随机（MPS）算法，用于对神经网络进行充分训练。