Copula-ResLogit: A Deep-Copula Framework for Unobserved Confounding Effects

arXiv cs.LG / 3/12/2026

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Key Points

Copula-ResLogit is proposed as a deep learning based fully interpretable joint modelling framework that combines Residual Neural Network (ResNet) architectures with copula models to address unobserved confounding in travel demand analysis.
The framework first detects unobserved confounding via traditional copula-based joint modelling and then mitigates hidden associations by incorporating deep learning components.
The authors validate the approach through two case studies: the relationship between stress levels and wait time for pedestrians crossing mid-block in VR, and the dependency between travel mode choice and travel distance in London data.
Results indicate that Copula-ResLogit substantially reduces or eliminates dependencies, demonstrating the effectiveness of residual layers in accounting for hidden confounding effects and enhancing interpretability of the joint model.

Abstract

A key challenge in travel demand analysis is the presence of unobserved factors that may generate non-causal dependencies, obscuring the true causal effects. To address the issue, the study introduces a novel deep learning based fully interpretable joint modelling framework, Copula-ResLogit, which integrates the flexibility of Residual Neural Network (ResNet) architectures with the dependence capturing capabilities of copula models. This hybrid structure enables us to first detect unobserved confounding through traditional copula function based joint modelling and then mitigate these hidden associations by incorporating deep learning components. The study applies this framework to two case studies, including the relationship between stress levels and wait time of pedestrians when crossing mid block in VR and the dependencies between travel mode choice and travel distance in London travel behaviour data. Results show that Copula-ResLogit substantially reduces or eliminates the dependencies, demonstrating the ability of residual layers to account for hidden confounding effects.