A variance-stabilizing coding scheme for spatial link matrices

In spatial statistics and spatial econometrics two coding schemes are used predominately Except for some initial work, the properties of both coding s chemes have not been investigated systematically. In this paper we do so fo r significant spatial processes specified as either a simultaneous autoregr essive or a moving average process. Results show that the C-coding scheme e mphasizes spatial objects with relatively large numbers of connections, suc h as those in the interior of a study region. In contrast, the W-coding sch eme assigns higher leverage to spatial objects with few connections, such a s those on the periphery of a study region. To address this topology-induce d heterogeneity, we design a novel S-coding scheme whose properties lie in between those of the C-coding and the W-coding schemes. To compare these th ree coding schemes within and across the different spatial processes, we fi nd a set of autocorrelation parameters that makes the processes stochastica lly homologous via a method based on the exact conditional expectation of M oran's I. In the new S-coding scheme the topology induced heterogeneity can be removed in tote for Moran's I as well as for moving average processes a nd it can be substantially alleviated for autoregressive processes.