A variance-stabilizing coding scheme for spatial link matrices

In spatial statistics and spatial econometrics two coding schemesare used predominately. Except for some initial work, the properties ofboth coding schemes have not been investigated systematically. In this paper we do so for significant spatial processes specifiedas either a simultaneous autoregressive or a moving average process. Resultsshow that the <i>C</i>-coding scheme emphasizes spatialobjects with relatively large numbers of connections, such as those inthe interior of a study region. In contrast, the <i>W</i>-coding scheme assigns higher leverage to spatial objects with few connections,such as those on the periphery of a study region. To address this topology-induced heterogeneity, we design a novel <i>S</i>-coding scheme whose properties lie in between thoseof the <i>C</i>-coding and the <i>W</i>-coding schemes. To compare these three coding schemes within and across thedifferent spatial processes, we find a set of autocorrelation parameters that makes the processes stochastically homologous via a methodbased on the exact conditional expectation of Moran's <i>I</i>. In the new <i>S</i>-coding scheme thetopology induced heterogeneity can be removed in toto for Moran's <i>I</i> as well as for moving average processes and it canbe substantially alleviated for autoregressive processes. <p>