getis {ecespa} | R Documentation |
Computes and plots the neighbourhood density function, a local version of the K-function defined by Getis and Franklin (1987).
getis(mippp, nx = 30, ny = 30, R = 10) ## S3 method for class 'ecespa.getis': plot(x, type="k", interp=100, color=tim.colors(64), contour=TRUE, points=TRUE,...)
mippp |
A point pattern. An object with the ppp format of spatstat . |
nx |
Grid dimensions (for estimation) in the x-side. |
ny |
Grid dimensions (for estimation) in the y-side. |
R |
Radius. The distance argument r at which the function K should be computed. |
x |
Result of applying getis to a point pattern. |
type |
Type of local statistics to be ploted. One of k (local-K), l (local-L), n (local-n) or d (deviations from CSR). |
interp |
Number of points in the side of the grid of points to interpolate the results. |
color |
A list of colors such as that generated by rainbow , heat.colors , topo.colors , terrain.colors or similar functions. |
contour |
Logical; if TRUE, add a contour to current plot. |
points |
Logical; if TRUE, add the point pattern to current plot. |
... |
Additional graphical parameters passed to link{plot} . |
Getis and Franklin (1987) proposed the neigbourhood density function, a local version of Ripley's L- function. Given a spatial point pattern X, the neigbourhood density function associated with the ith point in X is computed by
L[i](r) = sqrt((a/((n-1))*pi))*sum[j]e[i,j])
where the sum is over all points j != i that lie within a distance r of the ith point, a is the area of the observation window,
n is the number of points in X, and e[i,j] is the isotropic edge correction term (as described in Kest
). The value of L[i](r) can also
be interpreted as one of the summands that contributes to the global estimate of the L-function.
The command getis
actually computes the local K-function using Kcross
. As the main objective of getis
is to map the local density function,
as sugested by Gestis and Franklin (1987: 476) a grid of points (whose density is controled by nx
and ny
), is used to accurately estimate the
functions in empty or sparse areas. The S3 method plot.ecespa.getis
plots the spatial distribution of the local K or L function or other related local statistics, such as
n[i](r), the number of neighbor points [= lambda*K[i](r)] or the deviations from the expected value of local L under CSR [= L[i](r) -r]. It uses the function
interp
in akima
package to interpolate the results.
getis
gives an object of class ecespa.getis
, bassically a list with the following elements:
x |
x coordinates of pattern points (ahead) and grid points. |
y |
y coordinates of pattern points (ahead) and grid points. |
klocal |
Estimate of local K[i](r) at the point pattern points. |
klocalgrid |
Estimate of local K[i](r) at the grid points. |
R |
Distance r at which the estimation is made. |
nx |
Density of the estimating grid in the x-side. |
ny |
Density of the estimating grid in the x-side. |
dataname |
Name of the ppp object analysed. |
ppp |
Original point pattern. |
plot.ecespa.getis
plots an interpolated map of the selected local statistics
As plot.ecespa.getis
interpolates over rectangular grid of points, it is not apropriate to map irregular windows. In those cases, smooth.ppp
of spatstat
can be used to interpolate the local statistics (see examples).
Marcelino de la Cruz Rot marcelino.delacruz@upm.es
Getis, A. and Franklin, J. 1987. Second-order neighbourhood analysis of mapped point patterns. Ecology 68: 473-477
localK
, a different approach in spatstat.
## Not run: ## Compare with fig. 5b of Getis & Franklin (1987: 476): data(ponderosa) ponderosa12 <- getis(ponderosa, nx = 30, ny = 30, R = 12) plot(ponderosa12, type = "l") ## Plot the same, using smooth.ppp in spatstat ponderosa.12 <- setmarks(ponderosa, ponderosa12$klocal) Z <- smooth.ppp(ponderosa.12, sigma=5, dimyx=256) plot(Z, col=topo.colors(128), main="smoothed neighbourhood density") contour(Z, add=TRUE) points(ponderosa, pch=16, cex=0.5) ## Example with irregular window: data(letterR) X <- rpoispp(50, win=letterR) X.g <- getis(X, R=0.2) X2 <- setmarks(X, X.g$klocal) Z <- smooth.ppp(X2, sigma=0.05, dimxy=256) plot(Z, col=topo.colors(128), main="smoothed neighbourhood density") contour(Z, add=TRUE) points(X, pch=16, cex=0.5) ## End(Not run)