Sampling of alternatives in spatial decision contexts with logit and logit mixture models: Simulation and application to freshwater recreation in Germany

Destination choice modeling is challenging as the number of feasible sites is often very large. Sampling of alternatives has been used successfully to make large choice sets manageable and yields consistent estimates under certain conditions. However, the specific structure of destination choice data has rarely been addressed explicitly. Besides large numbers of alternatives, it is characterized by a skewed distribution of travel costs with few low-cost nearby sites and a disproportionate increase in alternatives with distance. In this paper, we investigate how this characteristic travel cost structure affects the quality of destination choice models estimated on samples of alternatives. Comparing uniform and strategic sampling (Lemp and Kockelman, 2012), we find that (i) strategic sampling reduces bias and improves efficiency relative to uniform sampling, (ii) sampling performance generally declines with stronger travel cost sensitivity, and (iii) the gains from strategic sampling increase as travel cost sensitivity becomes stronger. For multinomial logit, strategic sampling yields high levels of accuracy and precision when drawing as few as 10 out of 20,000 alternatives. For mixed logit, bias is higher, while the protocol still offers substantial performance gains. After presenting Monte Carlo evidence, we apply both sampling approaches to a nationwide freshwater recreation dataset and examine their impact on welfare estimates for two policy scenarios, as well as on bias and efficiency.