Failure to properly specify an agent's choice set in discrete choice models will generate biased parameter estimates resulting in inaccurate behavioral predictions as well as biased estimates of policy relevant metrics. We propose a method of constructing choice sets by sampling from specific points in space to model agent behavior when choice alternatives are unknown to the researcher, potentially infinite, and differ according to spatial and temporal factors. Using Monte Carlo analysis we compare the performance of this point-based sampling method to the commonly used approach of spatially aggregating choice alternatives. We then apply these alternative approaches to modelling location choice in the Pacific groundfish trawl fishery which has a complex spatial choice structure. Both the Monte Carlo and application results provide considerable support for the efficacy of the point-based approaches.