Evaluating the Performance of Spatially Explicit Models

Spatially explicit models are now widely used for conducting ecological research and for managing natural resources, due in part to the difficulty of undertaking empirical work at landscape scale. Unfortunately, error assessment and analysis of the predictive ability of such models is not well-developed, and has relied on the Kappa statistic and information-based measures. As has been pointed out, however, such approaches are limited by virtue of their global nature and weak hypotheses. As it turns out, the literature on map accuracy does provide a way of assessing model performance, and the goal of this paper is to adapt this literature to the need for evaluating the predictive ability of spatially explicit models. To this end, the paper first considers inference using the Kappa statistic. This is followed by a commentary on information theory, and a critique of both the Kappa statistic and information-based approaches given their global structure and underlying null hypotheses. A probabilistic treatment of alternative measures recently suggested follows, as does a direct adaptation of map inference to the modeling case. Examples of the proposed measures are given, using an application of logistic regression applied to land-cover changes that have recently occurred in the Muskegon River watershed of the State of Michigan.