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This study proposes an interpretable neural network-based non-proportionalodds model (N$^3$POM) for ordinal regression. N$^3$POM is different fromconventional approaches to ordinal regression with non-proportional models inseveral ways: (1) N$^3$POM is designed to directly handle continuous responses,whereas standard methods typically treat de facto ordered continuous variablesas discrete, (2) instead of estimating response-dependent finite coefficientsof linear models from discrete responses as is done in conventional approaches,we train a non-linear neural network to serve as a coefficient function. Thanksto the neural network, N$^3$POM offers flexibility while preserving theinterpretability of conventional ordinal regression. We establish a sufficientcondition under which the predicted conditional cumulative probability locallysatisfies the monotonicity constraint over a user-specified region in thecovariate space. Additionally, we provide a monotonicity-preserving stochastic(MPS) algorithm for effectively training the neural network. We apply N$^3$POMto several real-world datasets.

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