cor.spatial {SpatialPack}

Tjostheim's Coefficient

Description

Computes Tjostheim's coefficient for two spatial sequences observed over the same locations on the plane.

Usage

  cor.spatial(x, y, coords)

Arguments

x

an n-dimensional vector of data values.

y

an n-dimensional vector of data values.

coords

an n-by-2 matrix containing coordinates of the n data locations in each row.

Details

The implemented technique is a nonparametric coefficient that summarizes the association between two spatial variables. This coefficient was first introduced by Tjostheim (1978) and later generalized by Hubert and Golledge (1992). The computation of the coefficient is based on the construction of ranks associated to suitable modifications of the coordinates. Tjostheim's coefficient is a variant of the correlation coefficient (cor) to be used in a spatial statistics context.

Value

Tjostheim's coefficient. The variance is returned as the attribute "variance".

References

Tjostheim, D., (1978), A measure of association for spatial variables. Biometrika 65, 109-114.

Hubert, L., Golledge, R.G., (1982), Measuring association between spatially defined variables: Tjostheim's coefficient index and some extensions. Geographical Analysis 14, 273-278.

Examples

# Murray Smelter site dataset
data(murray)

# defining the arsenic (As) and lead (Pb) variables from the murray dataset
x <- murray$As
y <- murray$Pb

# extracting the coordinates from Murray dataset
coords <- murray[c("xpos","ypos")]

# computing Tjostheim's coefficient
z <- cor.spatial(x, y, coords)
z