Computes spatially-weighted versions of the the local multitype \(K\)-function or \(L\)-function.
localKcross.inhom(X, from, to,
lambdaFrom=NULL, lambdaTo=NULL,
..., rmax = NULL,
correction = "Ripley", sigma=NULL, varcov=NULL,
lambdaX=NULL, update=TRUE, leaveoneout=TRUE)
localLcross.inhom(X, from, to,
lambdaFrom=NULL, lambdaTo=NULL, ..., rmax = NULL)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
of type from.
The last two columns contain the r and theo values.
A point pattern (object of class "ppp").
Type of points from which distances should be measured.
A single value;
one of the possible levels of marks(X),
or an integer indicating which level.
Type of points to which distances should be measured.
A single value;
one of the possible levels of marks(X),
or an integer indicating which level.
Optional.
Values of the estimated intensity function
for the points of type from and to, respectively.
Each argument should be either a vector giving the intensity values
at the required points,
a pixel image (object of class "im") giving the
intensity values at all locations, a fitted point process model
(object of class "ppm") 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.
Optional arguments passed to density.ppp to control
the kernel smoothing procedure for estimating lambdaFrom
and lambdaTo, if they are missing.
Optional.
Values of the estimated intensity function
for all points of X.
Either a vector giving the intensity values
at each point of X,
a pixel image (object of class "im") giving the
intensity values at all locations, a list of pixel images
giving the intensity values at all locations for each type of point,
or a fitted point process model (object of class "ppm")
or a function(x,y) or function(x,y,m) which
can be evaluated to give the intensity value at any location.
Logical value indicating what to do when lambdaFrom,
lambdaTo or lambdaX 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.
Logical value (passed to density.ppp or
fitted.ppm) specifying whether to use a
leave-one-out rule when calculating the intensity.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
The functions localKcross.inhom and localLcross.inhom
are inhomogeneous or weighted versions of the
local multitype \(K\) and \(L\) functions implemented in
localKcross and localLcross.
Given a multitype spatial point pattern X,
and two designated types from and to,
the local multitype \(K\) function is
defined for each point X[i] that belongs to type from,
and is computed by
$$
K_i(r) = \sqrt{\frac 1 \pi \sum_j \frac{e_{ij}}{\lambda_j}}
$$
where the sum is over all points \(j \neq i\)
of type to 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 function
\(K_i(r)\) 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 of type from.
The corresponding \(L\) function \(L_i(r)\) is computed by applying the transformation \(L(r) = \sqrt{K(r)/(2\pi)}\).
Kinhom,
Linhom,
localK,
localL.
X <- amacrine
# compute all the local L functions
L <- localLcross.inhom(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)
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