Computes spatially-weighted versions of the the local \(K\)-function or \(L\)-function.
localKinhom(X, lambda, ..., rmax = NULL,
correction = "Ripley", verbose = TRUE, rvalue=NULL,
sigma = NULL, varcov = NULL, update=TRUE, leaveoneout=TRUE)
localLinhom(X, lambda, ..., rmax = NULL,
correction = "Ripley", verbose = TRUE, rvalue=NULL,
sigma = NULL, varcov = NULL, update=TRUE, leaveoneout=TRUE)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
the vector of values of the argument \(r\) at which the function \(K\) has been estimated
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.
A point pattern (object of class "ppp").
Optional.
Values of the estimated intensity function.
Either a vector giving the intensity values
at the points of the pattern X,
a pixel image (object of class "im") giving the
intensity values at all locations, a fitted point process model
(object of class "ppm" or "kppm" or "dppm")
or a function(x,y) which
can be evaluated to give the intensity value at any location.
Extra arguments. Ignored if lambda is present.
Passed to density.ppp if lambda is omitted.
Optional. Maximum desired value of the argument \(r\).
String specifying the edge correction to be applied.
Options are "none", "translate", "Ripley",
"translation", "isotropic" or "best".
Only one correction may be specified.
Logical flag indicating whether to print progress reports during the calculation.
Optional. A single value of the distance argument \(r\) at which the function L or K should be computed.
Optional arguments passed to density.ppp to control
the kernel smoothing procedure for estimating lambda,
if lambda is missing.
Logical value (passed to density.ppp or
fitted.ppm) specifying whether to use a
leave-one-out rule when calculating the intensity.
Logical value indicating what to do when lambda is a fitted model
(class "ppm", "kppm" or "dppm").
If update=TRUE (the default),
the model will first be refitted to the data X
(using update.ppm or update.kppm)
before the fitted intensity is computed.
If update=FALSE, the fitted intensity of the
model will be computed without re-fitting it to X.
Mike Kuhn, Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner r.turner@auckland.ac.nz
The functions localKinhom and localLinhom
are inhomogeneous or weighted versions of the
neighbourhood density function implemented in
localK and localL.
Given a spatial point pattern X, the
inhomogeneous neighbourhood density function
\(L_i(r)\) associated with the \(i\)th point
in X is computed by
$$
L_i(r) = \sqrt{\frac 1 \pi \sum_j \frac{e_{ij}}{\lambda_j}}
$$
where the sum is over all points \(j \neq i\) that lie
within a distance \(r\) of the \(i\)th point,
\(\lambda_j\) is the estimated intensity of the
point pattern at the point \(j\),
and \(e_{ij}\) 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
inhomogeneous L function (see Linhom).
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.
Kinhom,
Linhom,
localK,
localL.
X <- ponderosa
# compute all the local L functions
L <- localLinhom(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)
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