Revisiting Kappa to account for change in the accuracy assessment of land-use models

Land-use change models are typically calibrated to reproduce known historic changes. Calibration results can then be assessed by comparing two datasets: the simulated land-use map and the actual land-use map at the same time. A common method for this is the Kappa statistic, which expresses the agreement between two categorical datasets corrected for the expected agreement. This expected agreement is based on a stochastic model of random allocation given the distribution of class sizes. However, when a model starts from an initial land-use map and makes changes to it, that stochastic model does not pose a meaningful reference level. This paper introduces KSimulation, a statistic that is identical in form to the Kappa statistic but instead applies a more appropriate stochastic model of random allocation of class transitions relative to the initial map. The new method is illustrated on a simple example and then the results of the Kappa statistic and KSimulation are compared using the results of a land-use model. It is found that only KSimulation truly tests models in their capacity to explain land-use changes over time, and unlike Kappa it does not inflate results for simulations where little change takes place over time.