Spatial autocorrelation

Compute Moran's I or Geary's C measures of global spatial autocorrelation in a RasterLayer, or compute the the local Moran or Geary index (Anselin, 1995).

Usage

Geary(x, w=matrix(c(1,1,1,1,0,1,1,1,1), 3,3))
Moran(x, w=matrix(c(1,1,1,1,0,1,1,1,1), 3,3))
MoranLocal(x, w=matrix(c(1,1,1,1,0,1,1,1,1), 3,3))
GearyLocal(x, w=matrix(c(1,1,1,1,0,1,1,1,1), 3,3))

Arguments

x

RasterLayer

w

Spatial weights defined by or a rectangular matrix with odd length (3, 5, ...) sides (as in focal)

Value

A single value (Moran's I or Geary's C) or a RasterLayer (Local Moran or Geary values)

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.

See also

The spdep package for additional and more general approaches for computing indices of spatial autocorrelation

Author

Robert J. Hijmans and Babak Naimi

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

Examples

r <- raster(nrows=10, ncols=10)
values(r) <- 1:ncell(r)

Moran(r)
#> [1] 0.8353565
# Rook's case
f <- matrix(c(0,1,0,1,0,1,0,1,0), nrow=3)
Moran(r, f)
#> [1] 0.8929367

Geary(r)
#> [1] 0.04739631

x1 <- MoranLocal(r)

# Rook's case
x2 <- MoranLocal(r, w=f)