The housing search process, a topic of interest to both practitioners and researchers, starts with an alternative formation and screening practice. Due to the limitation of cognitive capacity, household members at this level evaluate potential alternatives based on many factors, such as lifestyle, preferences, and so on, to form a manageable choice set. This article attempts to provide a detailed study of this screening and filtering practice to develop a modeling framework that can replicate the choice set formation process. In order to show the potential of the method, one prospective decision criteria—the average desired commute to work distance—is considered the potential attribute that the household evaluates for feasible housing alternatives. It is postulated that alternatives will only be included in the choice set if the average work distance satisfies the household distance threshold. This article explores the viability of using proportional hazard models in the housing search process. Some of the specifications of hazard-based models that are typically used on temporal data are examined on average work distance. Several household sociodemographic attributes from eight waves of the Seattle Metropolitan Area’s Puget Sound Transportation Panel (PSTP) are utilized for model estimation, along with built environment variables, characteristics of the supply side of the market, and several other economic indicators. The approach presented in this article provides a remedy for the large choice set problem typically faced in discrete choice modeling.