Showing papers by "Barry Boots published in 2010"

A Note on the Extremities of Local Moran's Iis and Their Impact on Global Moran's I

Abstract: By defining local Moran's Iias a ratio of quadratic forms and making use of its overall additivity to match global Moran's I, we can identify spatial objects with a strong impact on global Moran's I. First, we concentrate on the spatial properties of local Moran's Iiexpressed by the local linkage degree. Depending on whether we use the W- or C-coding of the spatial connectivity matrix, the variance of local Moran's Iifor a small local linkage degree will be either large or small. Note that spatial objects associated with a local Moran's Iiwith a large variance affect the global statistic much more than spatial objects associated with a local Moran's Iiwith a small variance. Counterintuitively, global Moran's I defined in the W-coding is most influenced by spatial objects with a small number of spatial neighbors. In contrast, spatial objects with a large number of spatial neighbors exert more impact on global Moran's I setup in the C-coding. Second, we investigate the impact of the empirical data on local Moran's Iiand show that local Moran's Iiwill only be significant for extreme absolute residuals at and around the reference location. Clusters of average regression residuals cannot be detected by local Moran's Ii. Consequently, spatial cliques of extreme residuals contribute more to significance tests on global autocorrelation.

A Programming Approach to Minimizing and Maximizing Spatial Autocorrelation Statistics

Abstract: A programming approach is presented for identifying the form of the weights matrix W which either minimizes or maximizes the value of Moran's spatial autocorrelation statistic for a specified vector of data values. Both nonlinear and linear programming solutions are presented. The former are necessary when the sum of the links in W is unspecified while the latter can be used if this sum is fixed. The approach is illustrated using data examined in previous studies for two variables measured for the counties of Eire. While programming solutions involving different sets of constraints are derived, all yield solutions in which the number of nonzero elements in W is considerably smaller than that in W defined using the contiguity relationships between the counties. In graph theory terms, all of the Ws derived define multicomponent graphs. Other characteristics of the derived Ws are also presented.