localKinhom
Inhomogeneous Neighbourhood Density Function
Computes spatially-weighted versions of the the local \(K\)-function or \(L\)-function.
- Keywords
- spatial, nonparametric
Usage
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)
Arguments
- X
A point pattern (object of class
"ppp"
).- lambda
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 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.- 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.
- sigma, varcov
Optional arguments passed to
density.ppp
to control the kernel smoothing procedure for estimatinglambda
, iflambda
is missing.- leaveoneout
Logical value (passed to
density.ppp
orfitted.ppm
) specifying whether to use a leave-one-out rule when calculating the intensity.- update
Logical value indicating what to do when
lambda
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
.
Details
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
.
Value
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
See Also
Examples
# NOT RUN {
data(ponderosa)
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)
# }