Path dependence and the validation of agent-based spatial models of land use

In this paper, we identify two distinct notions of accuracy of land-use models and highlight a tension between them. A model can have predictive accuracy: its predicted land-use pattern can be highly correlated with the actual land-use pattern. A model can also have process accuracy: the process by which locations or land-use patterns are determined can be consistent with real world processes. To balance these two potentially conflicting motivations, we introduce the concept of the invariant region, i.e., the area where land-use type is almost certain, and thus path independent; and the variant region, i.e., the area where land use depends on a particular series of events, and is thus path dependent. We demonstrate our methods using an agent-based landuse model and using multi-temporal land-use data collected for Washtenaw County, Michigan, USA. The results indicate that, using the methods we describe, researchers can improve their ability to communicate how well their model performs, the situations or instances in which it does not perform well, and the cases in which it is relatively unlikely to predict well because of either path dependence or stochastic uncertainty.