An interpretable neural network-based non-proportional odds model for ordinal regression with continuous response

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.