Publication: A fuzzy set approach to assess the predictive accuracy of land use simulations

doi:10.1016/j.ecolmodel.2013.03.019

Abstract

The predictive accuracy of land use models is frequently assessed by comparing two data sets: the sim-ulated land use map and the observed land use map at the end of the simulation period. A commonstatistic for this is Kappa, which expresses the agreement between two categorical maps, corrected forthe agreement as can be expected by chance. This chance agreement is based on a stochastic model ofrandom allocation given the distribution of class sizes. Two existing statistics extend Kappa to make itmore appropriate for the assessment of land use models: Fuzzy Kappa uses fuzzy set theory to includedegrees of similarity, which adds geographical nuance because it distinguishes between small and largedisagreement in position and in land use classes. Kappa Simulation, on the other hand, addresses thestochastic model that underlies the expected agreement: when a model starts from an initial land usemap and subsequently makes changes to it, a stochastic model of random allocation given the distribu-tion of class sizes has little relevance. The expected accuracy in Kappa Simulation is therefore based ontransition probabilities relative to the initial map. This paper presents Fuzzy Kappa Simulation, a statisticthat combines the geographical nuance of Fuzzy Kappa with the stochastic model of Kappa Simulation.This new statistic is demonstrated on a case study example and results are compared with other vari-ations of Kappa. The comparison confirms that Fuzzy Kappa Simulation is the only statistic to evaluatemodels in terms of land use transitions, while also being sensitive to geographical nuance.

Keywords

Land use model; Accuracy assessment; Fuzziness; Map comparison; Kappa statistics