linearpcfinhom
Inhomogeneous Linear Pair Correlation Function
Computes an estimate of the inhomogeneous linear pair correlation function for a point pattern on a linear network.
- Keywords
- spatial, nonparametric
Usage
linearpcfinhom(X, lambda=NULL, r=NULL, ..., correction="Ang",
normalise=TRUE, normpower=1,
update = TRUE, leaveoneout = TRUE,
ratio = FALSE)
Arguments
- X
Point pattern on linear network (object of class
"lpp"
).- lambda
Intensity values for the point pattern. Either a numeric vector, a
function
, a pixel image (object of class"im"
) or a fitted point process model (object of class"ppm"
or"lppm"
).- r
Optional. Numeric vector of values of the function argument \(r\). There is a sensible default.
- …
Arguments passed to
density.default
to control the smoothing.- correction
Geometry correction. Either
"none"
or"Ang"
. See Details.- normalise
Logical. If
TRUE
(the default), the denominator of the estimator is data-dependent (equal to the sum of the reciprocal intensities at the data points, raised tonormpower
), which reduces the sampling variability. IfFALSE
, the denominator is the length of the network.- normpower
Integer (usually either 1 or 2). Normalisation power. See explanation in
linearKinhom
.- update
Logical value indicating what to do when
lambda
is a fitted model (class"lppm"
or"ppm"
). Ifupdate=TRUE
(the default), the model will first be refitted to the dataX
(usingupdate.lppm
orupdate.ppm
) 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
fitted.lppm
orfitted.ppm
) specifying whether to use a leave-one-out rule when calculating the intensity, whenlambda
is a fitted model. Supported only whenupdate=TRUE
.- ratio
Logical. If
TRUE
, the numerator and denominator of each estimate will also be saved, for use in analysing replicated point patterns.
Details
This command computes the inhomogeneous version of the linear pair correlation function from point pattern data on a linear network.
If lambda = NULL
the result is equivalent to the
homogeneous pair correlation function linearpcf
.
If lambda
is given, then it is expected to provide estimated values
of the intensity of the point process at each point of X
.
The argument lambda
may be a numeric vector (of length equal to
the number of points in X
), or a function(x,y)
that will be
evaluated at the points of X
to yield numeric values,
or a pixel image (object of class "im"
) or a fitted point
process model (object of class "ppm"
or "lppm"
).
If lambda
is a fitted point process model,
the default behaviour is to update the model by re-fitting it to
the data, before computing the fitted intensity.
This can be disabled by setting update=FALSE
.
If correction="none"
, the calculations do not include
any correction for the geometry of the linear network.
If correction="Ang"
, the pair counts are weighted using
Ang's correction (Ang, 2010).
The bandwidth for smoothing the pairwise distances
is determined by arguments …
passed to density.default
, mainly the arguments
bw
and adjust
. The default is
to choose the bandwidth by Silverman's rule of thumb
bw="nrd0"
explained in density.default
.
Value
Function value table (object of class "fv"
).
If ratio=TRUE
then the return value also has two
attributes called "numerator"
and "denominator"
which are "fv"
objects
containing the numerators and denominators of each
estimate of \(g(r)\).
References
Ang, Q.W. (2010) Statistical methodology for spatial point patterns on a linear network. MSc thesis, University of Western Australia.
Ang, Q.W., Baddeley, A. and Nair, G. (2012) Geometrically corrected second-order analysis of events on a linear network, with applications to ecology and criminology. Scandinavian Journal of Statistics 39, 591--617.
Okabe, A. and Yamada, I. (2001) The K-function method on a network and its computational implementation. Geographical Analysis 33, 271-290.
See Also
Examples
# NOT RUN {
data(simplenet)
X <- rpoislpp(5, simplenet)
fit <- lppm(X ~x)
K <- linearpcfinhom(X, lambda=fit)
plot(K)
# }