R: Spatial autocorrelation

autocorrelation {raster} | R Documentation

## Spatial autocorrelation

### Description

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`)

### 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.

### Value

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

### Author(s)

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

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

### See Also

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

### Examples

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

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

    Geary(r)

    x1 <- MoranLocal(r)

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

[Package raster version 3.3-7 Index]