Simplified probabilistic choice set formation models in a residential location choice context

The implementation of a theoretically sound, two-stage discrete-choice modelling paradigm incorporating probabilistic choice sets is impractical when the number of alternatives is large, which is a typical case in most spatial choice contexts. In the context of residential location choice, Kaplan et al. (2009), (2011), (2012) (KBS) developed a semi-compensatory choice model incorporating data of individuals searching for dwellings observed using a customised real estate agency website. This secondary data is used to compute the probability of considering a choice set that takes the form of an ordered probit model. In this paper, we illustrate that the simplicity of the KBS model arises because of an unrealistic assumption that individuals' choice sets only contain alternatives that derive from their observed combination of thresholds. Relaxing this assumption, we introduce a new probabilistic choice set formation model that allows the power set to include all potential choice sets derived from variations in thresholds' combinations. In addition to extending the KBS model, our proposed model asymptotically approaches the classical Manski model, if a suitable structure is used to categorise alternatives. In order to illustrate the biases inherent in the original KBS approach, we compare it with our proposed model and the MNL model using a Monte Carlo experiment. The results of this experiment show that the KBS model causes biases in predicted market share if individuals are free to choose from any potential choice sets derived from combinations of thresholds.