Conceptual Foundations of Spatial Choice Models

As the location choice of an individual determines his or her feasible consumption set, it can be modelled as a two-stage procedure. First, the individual finds an optimal consumption bundle for each one of the feasible consumption sets that correspond to the locations considered. Second, he or she compares the resulting location-specific optimal utility levels and chooses a location for which the optimal utility level is a maximum. It is imagined that an observer applies costless sampling of the feasible consumption sets involved and records the individual's utility level associated with each trial. As the sample can be arbitrarily large, the asymptotic theory of extremes may be used in order to compute the probability that the consumption bundle associated with the highest overall utility level will correspond to any particular location. The way in which different sampling designs generate different choice probability models either in discrete or in continuous geographical space is explained. The multinomial logit model emerges when perfectly even sampling is applied on a discrete spatial choice set.