Modeling and interpreting the accuracy assessment error matrix for a doubly classified map

Abstract

This paper considers two maps having the same spatial extent and the same mapping categories but where each map is subject to classification error. An overlay of the maps yields a (dis)similarity matrix whose (i, j)-entry is the areal proportion placed into category i by the first map and into category j by the second map. A parametric model, called the latent truth model, is proposed which specifies the dissimilarity matrix in terms of the true (but unknown) proportions for the mapping categories as well as the unknown error rates for the two maps. The number of parameters in the model exceeds the degrees of freedom in the dissimilarity matrix. However, a method of regularization is applied to effectively reduce the dimension of the parameter space and to permit model fitting. From the fitted model, one obtains estimates for the true mapping proportions as well as estimated error matrices for each of the maps. Accuracy assessment characteristics for each map (such as user's accuracy, producer's accuracy, overall accuracy, and the kappa coefficient) can be computed from the estimated error matrices. Methods are illustrated with two landcover maps of Wicomico County, Maryland.