ACCOUNTING FOR THE CONSIDERATION SET IN DISCRETE CHOICE MODELS BASED ON HISTORICAL CHOICES

Abstract

The consideration set represents the subset of alternatives that individuals evaluate when choosing becomes impractical when facing a large number of options, a challenge that is common to various transportation models of route or schedule choices. Since this set is latent to the researcher, explaining it adequately is crucial for achieving consistent parameter estimation in discrete choice models. While theoretically robust methods to construct the consideration set are often impractical, existing practical approaches lack theoretical foundation. This article aims to bridge that gap. This article provides a theoretical basis for constructing consideration sets using historical or cohortbased choices, leveraging data from passive sources such as mobile phones, travel smart cards, and credit card records. Building on McFadden's sampling of alternatives theorem, the study establishes the necessary conditions for consistent estimation of model parameters when using this historical cohort approach. Specifically, it demonstrates how assumptions of behavioral, consideration, and attribute invariability can link the latent consideration set problem to the sampling of alternatives problem, enabling consistent parameter estimation. Monte Carlo simulations illustrate the effects of varying sample sizes, the impact of correction methods, and the consequences of assumption violations. Additionally, a variation of Chamberlain's fixed-effects model is proposed to address scenarios where attribute values and choice probabilities vary over time. Practical recommendations are provided to balance the trade-off between data recency and stability of assumptions, offering a robust framework for latent consideration set modeling in diverse applications.