Neighbourhood density function
Computes the neighbourhood density function, a local version of the K-function or L-function, defined by Getis and Franklin (1987).
localK(X, ..., rmax = NULL, correction = "Ripley", verbose = TRUE, rvalue=NULL) localL(X, ..., rmax = NULL, correction = "Ripley", verbose = TRUE, rvalue=NULL)
X |
A point pattern (object of class |
... |
Ignored. |
rmax |
Optional. Maximum desired value of the argument r. |
correction |
String specifying the edge correction to be applied.
Options are |
verbose |
Logical flag indicating whether to print progress reports during the calculation. |
rvalue |
Optional. A single value of the distance argument r at which the function L or K should be computed. |
The command localL computes the neighbourhood density function,
a local version of the L-function (Besag's transformation of Ripley's
K-function) that was proposed by Getis and Franklin (1987).
The command localK computes the corresponding
local analogue of the K-function.
Given a spatial point pattern X, the neighbourhood density function
L[i](r) 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 an 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.
By default, the function L[i](r) or
K[i](r) is computed for a range of r values
for each point i. The results are stored as a function value
table (object of class "fv") with a column of the table
containing the function estimates for each point of the pattern
X.
Alternatively, if the argument rvalue is given, and it is a
single number, then the function will only be computed for this value
of r, and the results will be returned as a numeric vector,
with one entry of the vector for each point of the pattern X.
Inhomogeneous counterparts of localK and localL
are computed by localKinhom and localLinhom.
If rvalue is given, the result is a numeric vector
of length equal to the number of points in the point pattern.
r |
the vector of values of the argument r at which the function K has been estimated |
theo |
the theoretical value K(r) = pi * r^2 or L(r)=r for a stationary Poisson process |
together with columns containing the values of the
neighbourhood density function for each point in the pattern.
Column i corresponds to the ith point.
The last two columns contain the r and theo values.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
Getis, A. and Franklin, J. (1987) Second-order neighbourhood analysis of mapped point patterns. Ecology 68, 473–477.
data(ponderosa) X <- ponderosa # compute all the local L functions L <- localL(X) # plot all the local L functions against r plot(L, main="local L functions for ponderosa", legend=FALSE) # plot only the local L function for point number 7 plot(L, iso007 ~ r) # compute the values of L(r) for r = 12 metres L12 <- localL(X, rvalue=12) # Spatially interpolate the values of L12 # Compare Figure 5(b) of Getis and Franklin (1987) X12 <- X %mark% L12 Z <- Smooth(X12, sigma=5, dimyx=128) plot(Z, col=topo.colors(128), main="smoothed neighbourhood density") contour(Z, add=TRUE) points(X, pch=16, cex=0.5)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.