Models of count with endogenous choices

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 sites, for example transit stations and public parks. From a modeling perspective, these data are aggregate counts at the top level, but are 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 examines discretionary activity type choice for activities completed within a one-day period. The results show that a model of count with endogenous choices can account for the mapping of impacts of choice attributes from the lower level towards the observed count at the top level emerging from choices, including the idiosyncratic term associated with the utility of choice alternatives. Furthermore, since this model preserves the linkage between the maximizing utility and rate parameter in the joint model, identifying the contribution of attributes between the two levels is possible.