Investigating Global and Local Categorical Map Configuration Comparisons Based on Coincidence Matrices T. K. Remmel Department of Geography, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3 The simple and intuitive nature of the coincidence matrix has not only made it the current ‘‘gold standard’’ for accuracy assessment (based on a sample of map pixels), but also a common tool for describing difference between two categorical maps (when all pixels are enumerated). It is this latter case of map comparison that this article explores. Coincidence matrices, although providing significant information regarding thematic agreement between two categorical maps (composition), can lack signifi- cantly in terms of conveying information about differences or similarities in the spatial arrangement (configuration) of those map categories in geographic space. This article introduces means for distilling the available configuration information from a coinci- dence matrix while demonstrating some simple categorical map comparisons. Spe- cifically, while the coincidence matrix summarizes per-pixel compositional persistence or change, the introduced technique further quantifies the global and local configurational uncertainty between compared maps. I demonstrate how this quantification of configurational uncertainty can be used to gauge which thematic mismatch types are most significant and how to measure/present local configurational uncertainty in a spatial context. Implementation is through a straightforward mathe- matical algorithm in R that is illustrated by several examples. Introduction A coincidence matrix, also referred to as an error or confusion matrix (Congalton 1991; Stehman 1997; Foody 2002), is typically used to summarize the cor- respondence of labels assigned to geographic sites (e.g., pixel categories) with reference data. Generally, the construction of a coincidence matrix relies on a representative sample of locations (Stehman and Czaplewski 1998) intended to capture the true character (and configurational distribution) of the data. In cases where the entire population of pixels between two categorical maps is cross Correspondence: T. K. Remmel, Department of Geography, York University, 4700 Keele Street, Toronto, Ontario, Canada M3J 1P3 e-mail: remmelt@yorku.ca Submitted: June 11, 2007. Revised version accepted: December 14, 2007. Geographical Analysis 41 (2009) 144–157 r 2009 The Ohio State University 144 Geographical Analysis ISSN 0016-7363