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The problem of choice set formation for decision makers is an important subject in discrete choice modeling, especially when the choice set contains a large number of elemental alternatives. In general, the choice set of an individual could be a randomly sampled choice set; however, this is claimed to be a behaviorally unacceptable practice because of the fallacious assumption of individuals’ full knowledge of potential random choices. This issue brings up the need to devise methods to logically allocate credible choice alternatives for individuals. Although the use of these methods could be dependent on specific applications, this study attempted to identify the distinction between model estimation and prediction steps in the context of residential location choice modeling. From a theoretical point of view, the paper proposes a modified weighted stratified sampling approach that is an improved version of random sampling for model estimation. The approach is believed to be a better replicate of the universal choice set than other sampling methods, and it is capable of resulting in consistent estimates even with small sample sizes. The estimated model was applied in a simulation framework with a hazard-based imputed choice set approach for prediction.

Hazard models are used only moderately in the transportation field compared with their levels of application in other areas, such as medicine, political science, and economics. Many specifications of the hazard models are not well known, whereas the primary application of hazard models is limited to a basic proportional continuous hazard formulation with continuous failure time and Weibull baseline hazard function. Besides the recent advances in the methodology of hazard-based models, the basic proportional hazard formulation remains the proffered hazard-based modeling approach. This paper aims to present some popular specifications of hazard-based models and also discusses some formulations that are less frequently used in practical models. In this study, the Weibull baseline hazard, which is a monotonic function, is replaced by the nonmonotonic log logistic function, and the modified formulation is presented. The log logistic and Weibull formulations are also presented, not only in continuous form but also in discrete hazard formulations for applications in which the failures are observed in discrete time intervals. Finally, all four combinations of discrete and continuous formulations with Weibull and log logistic baselines are discussed with the option of unobserved heterogeneity of type of gamma distribution. The accelerated failure time model, which is an alternative to the proportional hazard models, is discussed. This paper attempts to present a comprehensive overview of the applications of the duration model in the field of transportation.