Cliff and Ord (1969), published forty years ago, marked a turning point in the treatment of spatial autocorrelation in quantitative geography. It provided the framework needed by any applied researcher to attempt an implementation for a different system, possibly using a different programming language. In this spirit, here we examine how spatial weights have been represented in implementations and may be reproduced, how the tabulated results in the paper may be reproduced, and how they may be extended to cover simulation.
One of the major assertions of Cliff and Ord (1969) is that their statistic advances the measurement of spatial autocorrelation with respect to Moran (1950) and Geary (1954) because a more general specification of spatial weights could be used. This more general form has implications both for the preparation of the weights themselves, and for the calculation of the measures. We will look at spatial weights first, before moving on to consider the measures presented in the paper and some of their subsequent developments. Before doing this, we will put together a data set matching that used in Cliff and Ord (1969). They provide tabulated data for the counties of the Irish Republic, but omit Dublin from analyses. A shapefile included in this package, kindly made available by Michael Tiefelsdorf, is used as a starting point:
library(spdep)
eire <- as(sf::st_read(system.file("shapes/eire.shp", package="spData")[1]), "Spatial")
row.names(eire) <- as.character(eire$names)
proj4string(eire) <- CRS("+proj=utm +zone=30 +ellps=airy +units=km")class(eire)## [1] "SpatialPolygonsDataFrame"
## attr(,"package")
## [1] "sp"names(eire)## [1] "A" "towns" "pale" "size" "ROADACC" "OWNCONS" "POPCHG"
## [8] "RETSALE" "I