Nonlinear determinants of discretionary activity episodes in non-mandatory tours

A Neural-Network-embedded Generalised Ordered Response Probit (NNGORP) model captures nonlinear effects on latent propensity for ordered activity frequency outcomes. Jointly learning latent propensity and thresholds, it embeds neural representations into a probabilistic latent-index structure for counts, preserving a coherent discrete distribution over non-negative integers while capturing complex nonlinearities. Simulations verify accurate parameter and marginal effect recovery from a benchmark GORP. It models discretionary activity frequency using 60,309 tours from the 2019 Shanghai Household Travel Survey including sociodemographic, household, and built-environment variables. Results reveal nonlinearities and threshold responses for age, household employment, young children, bicycle ownership, and neighbourhood density. Structurally derived from the latent-index mechanism, partial dependence patterns reflect genuine behavioural processes rather than post-hoc approximations. Behavioural interpretation confirms structurally derived patterns provide more coherent, generalisable insights than SHAP from conventional ML. These findings deepen understanding of discretionary activity generation in high-density urban settings, informing travel demand management and planning.