Pontius, R. Gil Jr. In Review. A statistical method to partition effects of quantity from location in comparison of categorical maps at multiple resolutions. International Journal of Geographic Information Systems. Volume ?? (Issue ??):Pages ??.


A Statistical Method to Partition Effects of Quantity from Location in Comparison of Categorical Maps at Multiple Resolutions

R Gil Pontius Jr

Abstract

This paper presents new generalized statistical methods to measure agreement between two maps at multiple-resolutions, where each cell in each map has a multinomial distribution among any number of land types. This methodology quantifies agreement between any two categorical maps, where either map uses fuzzy or hard classification. The method measures the agreement at various resolutions, by aggregating neighboring cells into an increasingly coarse grid. At each resolution, the method partitions the overall agreement into: agreement due to chance, agreement due to quantity, agreement due to location, error due to location, and error due to quantity. This partitioning is plotted in a three dimensional space where the axes are: 1) percent agreement, as a function of 2) resolution, and 3) quantity of a specific land type in one of the maps. In addition, the method computes six statistics that are useful to interpret the differences between maps, and shows how these statistics change with resolution. The method is valuable for any GIS professional who needs to compare maps in terms of quantity and location at multiple resolutions. For illustration, this paper applies these theoretical concepts to the validation of a land-use change model for Costa Rica.

Keywords

accuracy assessment, fuzzy sets, kappa, scale, value of perfect information

Figures

See the figures page for this paper.

 

Copyright 2000 Graduate School of Geography, Clark University