ABSTRACT
In many instances, one encounters the need to study the elapsed time until the occurrence of an event or the duration of an event. Data such as these are referred to as duration data and are encountered often in the field of transportation research. Examples include the time until a vehicle accident occurs, the time between vehicle purchases, the time devoted to an activity (shopping, recreational, etc.), and the time until the adoption of new transportation technologies. Duration data are usually continuous and can, in most cases, be modeled using least-squares regression. The use of estimation techniques that are based on hazard functions, however, can often provide additional insights into the underlying duration problem. This chapter explores the wide variety of hazard-based duration models including non-parametric, semi-parametric, and fully parametric models. The Cox proportional hazards model along with the Weibull, exponential, and log-logistic distributions are considered. Extensions to account for heterogeneity across observations are also presented (the Weibull model with gamma heterogeneity). The chapter provides numerous examples to show how these models are applied.
