Practical limits of Moran's autocorrelation index for raster class maps

This paper is concerned with the calculation of the Moran index of spatial contiguity, also known as Moran's I, on binary raster maps. While the theoretical range of I extends from roughly -1 to 1 for a raster map, in practice possible I values are much more restricted. The nature of the restriction is due to the rigid cell framework, which defines contiguity, as well as the relative proportions of ones to zeros in the binary raster. This paper presents experimental findings demonstrating the practical limits of Moran's I under a variety of different proportions and contiguity measures. Results for negatively autocorrelated surfaces are particularly noteworthy; unequal proportions of ones and zeros can result in minimal I values considerably larger than -1, and in many cases considerably larger than 0. Implications for the use of I on raster maps are considered, as is the potential relevance of negative spatial autocorrelation and its measurement. (c) 2006 Elsevier Ltd. All rights reserved.