Spatial autocorrelation

Compute spatial autocorrelation for a numeric vector or a SpatRaster. You can compute standard (global) Moran's I or Geary's C, or local indicators of spatial autocorrelation (Anselin, 1995).

Usage

# S4 method for class 'numeric'
autocor(x, w, method="moran")

# S4 method for class 'SpatRaster'
autocor(x, w=matrix(c(1,1,1,1,0,1,1,1,1),3), method="moran", global=TRUE)

Arguments

x: numeric or SpatRaster
w: Spatial weights defined by or a rectangular matrix. For a SpatRaster this matrix must the sides must have an odd length (3, 5, ...)
global: logical. If TRUE global autocorrelation is computed instead of local autocorrelation
method: character. If x is numeric or SpatRaster: "moran" for Moran's I and "geary" for Geary's C. If x is numeric also: "Gi", "Gi*" (the Getis-Ord statistics), locmor (local Moran's I) and "mean" (local mean)

Value

numeric or SpatRaster

Details

The default setting uses a 3x3 neighborhood to compute "Queen's case" indices. You can use a filter (weights matrix) to do other things, such as "Rook's case", or different lags.

References

Moran, P.A.P., 1950. Notes on continuous stochastic phenomena. Biometrika 37:17-23

Geary, R.C., 1954. The contiguity ratio and statistical mapping. The Incorporated Statistician 5: 115-145

Anselin, L., 1995. Local indicators of spatial association-LISA. Geographical Analysis 27:93-115

https://en.wikipedia.org/wiki/Indicators_of_spatial_association

Examples

### raster
r <- rast(nrows=10, ncols=10, xmin=0)
values(r) <- 1:ncell(r)

autocor(r)
#>     lyr.1 
#> 0.8362573 

# rook's case neighbors
f <- matrix(c(0,1,0,1,0,1,0,1,0), nrow=3)
autocor(r, f)
#>     lyr.1 
#> 0.8888889 

# local 
rc <- autocor(r, w=f, global=FALSE)

### numeric (for vector data)
f <- system.file("ex/lux.shp", package="terra")
v <- vect(f)
w <- relate(v, relation="touches")

# global
autocor(v$AREA, w)
#> [1] -0.1531971

# local
v$Gi <- autocor(v$AREA, w, "Gi") 
plot(v, "Gi")