Resumen
In transportation and traffic analysis count data arises frequently, collectively emerging from individual traveler choices from a choice set of alternatives. Examples include network origin-destination (OD) flow rates and visitor counts at transit stations. From a modeling perspective, these data are aggregate counts at the top level, but comprised of individual discrete choices at the lower level. Models of count data are widely applied in the transportation and traffic fields. However, only a moderate level of applications jointly model count observations at the top level with discrete choice models at the bottom level under a random utility maximization (RUM) framework. This paper considers modeling count data with an underlying choice process as a joint model that merges an observed event count process with a discrete choice process, where the count level is Poisson distributed. This model captures both processes within a single random utility framework that preserves a direct mapping between the count intensity and the utility of the chosen alternative, including unobserved variables and latent factors. The decision-making context presented examines discretionary activity type choice for activities completed within a one-day period. The estimation results for this model are compared against (i) a mixed-logit model and (ii) a mixed-Poisson model, each with normally distributed parameters. The results indicate that a model of count with endogenous choices can account for the randomness associated with the utility of choice alternatives from lower level discrete choices, consequently leading to significantly different utility parameter estimates for the Poisson rate parameter in the upper level. Furthermore, while the linkage between the maximizing utility and rate parameter is preserved in this joint model, identifying the contribution of attributes between the two levels requires further parameterization.