An Interpretable Neural Network-based Nonproportional Odds Model for Ordinal Regression

This study proposes an interpretable neural network-based nonproportional odds model (N³POM) for ordinal regression. N³POM is different from conventional approaches to ordinal regression with nonproportional models in several ways: (a) N³POM is defined for both continuous and discrete responses, whereas standard methods typically treat the continuous variables as if they were discrete, (b) instead of estimating response-dependent finite-dimensional coefficients of linear models from discrete responses as is done in conventional approaches, we train a nonlinear neural network to serve as a coefficient function. Thanks to the neural network, N³POM offers flexibility while preserving the interpretability of conventional ordinal regression. We establish a sufficient condition under which the predicted conditional cumulative probability locally satisfies the monotonicity constraint over a user-specified region in the covariate space. Additionally, we provide a monotonicity-preserving stochastic (MPS) algorithm for effectively training the neural network. We apply N³POM to several real-world datasets. Supplementary materials for this article are available online.