localK | R Documentation |
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.
If rvalue
is absent, the result is
an object of class "fv"
, see fv.object
,
which can be plotted directly using plot.fv
.
Essentially a data frame containing columns
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 i
th point.
The last two columns contain the r
and theo
values.
and \rolf
Getis, A. and Franklin, J. (1987) Second-order neighbourhood analysis of mapped point patterns. Ecology 68, 473–477.
Kest
,
Lest
,
localKinhom
,
localLinhom
.
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)
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