An interpretable neural network-based non-proportional odds model for ordinal regression
Abstract: This study proposes an interpretable neural network-based non-proportional odds model (N$3$POM) for ordinal regression. N$3$POM is different from conventional approaches to ordinal regression with non-proportional models in several ways: (1) N$3$POM is defined for both continuous and discrete responses, whereas standard methods typically treat the ordered continuous variables as if they are discrete, (2) instead of estimating response-dependent finite-dimensional coefficients of linear models from discrete responses as is done in conventional approaches, we train a non-linear neural network to serve as a coefficient function. Thanks to the neural network, N$3$POM 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 N$3$POM to several real-world datasets.
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