A hierarchical Bayesian discrete–continuous mixture model with nested Dirichlet processes

Discrete choice models typically represent preference heterogeneity as either continuous random coefficients or discrete latent classes. Nevertheless, numerous real-world choice contexts are characterized by regime level and within-regime heterogeneity. This paper proposes a nested Dirichlet process prior hierarchical Bayesian discrete–continuous latent class choice model in which the numbers of macro regimes and micro classes can be estimated from the data. Truncated variational Bayes with local Laplace updates is used for estimation. A Monte Carlo study with 1,500 individuals, 6 choice occasions, and 3 alternatives is used to evaluate the model's performance via a train-test validation process, reporting held-out log-likelihood and clustering accuracy scores. The proposed model has better performance in latent structure recovery and predictive performance over multinomial logit, mixed logit, and latent class benchmarks. Similar held-out prediction gains are observed on an application to the Swissmetro dataset. Overall, the findings suggest that behavioural interpretability and predictive accuracy improve when modelling accounts for layered heterogeneity.