A neural estimation framework for discrete choice models with arbitrary error distributions

This paper presents RUM-NN, a neural network framework that is fully consistent with the Random Utility Maximisation (RUM) theory and designed to flexibly model discrete choice behaviour under a wide range of error distributions. RUM-NN contributes a flexible estimation approach to accommodate arbitrary error distributions. This enables the modelling of choice probabilities even when closed-form solutions are unavailable, accommodating arbitrary error structures, including correlated and non-conventional distributions. The proposed RUM-NN is introduced in both linear and non-linear structures. The linear version of RUM-NN retains interpretability similar to traditional econometric models, while the nonlinear extension enhances predictive flexibility by capturing complex relationships in the utility function. The performance of RUM-NN in parameter recovery and prediction accuracy is rigorously evaluated using synthetic datasets through Monte Carlo experiments. Additionally, RUM-NN is evaluated on the Swissmetro and the London Passenger Mode Choice (LPMC) datasets with different sets of distribution assumptions for the error component. The results demonstrate that RUM-NN under linear utility structure and IID Gumbel error terms can replicate the performance of Multinomial Logit model, but relaxing those constraints yields to superior performance for both Swissmetro and LMPC datasets. By introducing a novel estimation approach aligned with statistical theories, this study empowers econometricians to harness the advantages of neural network models. To facilitate the implementation of RUM-NN, a Python library has been developed and made publicly available.