localKcross.inhom
Inhomogeneous Multitype K Function
Computes spatially-weighted versions of the the local multitype \(K\)-function or \(L\)-function.
- Keywords
- spatial, nonparametric
Usage
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)
Arguments
- X
A point pattern (object of class
"ppp"
).- from
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.- to
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.- lambdaFrom,lambdaTo
Optional. Values of the estimated intensity function for the points of type
from
andto
, 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 afunction(x,y)
which can be evaluated to give the intensity value at any location.- …
Extra arguments. Ignored if
lambda
is present. Passed todensity.ppp
iflambda
is omitted.- rmax
Optional. Maximum desired value of the argument \(r\).
- correction
String specifying the edge correction to be applied. Options are
"none"
,"translate"
,"Ripley"
,"translation"
,"isotropic"
or"best"
. Only one correction may be specified.- sigma, varcov
Optional arguments passed to
density.ppp
to control the kernel smoothing procedure for estimatinglambdaFrom
andlambdaTo
, if they are missing.- lambdaX
Optional. Values of the estimated intensity function for all points of
X
. Either a vector giving the intensity values at each point ofX
, 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 afunction(x,y)
orfunction(x,y,m)
which can be evaluated to give the intensity value at any location.- update
Logical value indicating what to do when
lambdaFrom
,lambdaTo
orlambdaX
is a fitted model (class"ppm"
,"kppm"
or"dppm"
). Ifupdate=TRUE
(the default), the model will first be refitted to the dataX
(usingupdate.ppm
orupdate.kppm
) before the fitted intensity is computed. Ifupdate=FALSE
, the fitted intensity of the model will be computed without re-fitting it toX
.- leaveoneout
Logical value (passed to
density.ppp
orfitted.ppm
) specifying whether to use a leave-one-out rule when calculating the intensity.
Details
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 \(L(r) = \sqrt{K(r)/(2\pi)}\).
Value
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
See Also
Examples
# NOT RUN {
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)
# }