Ginhom
Inhomogeneous Nearest Neighbour Function
Estimates the inhomogeneous nearest neighbour function \(G\) of a non-stationary point pattern.
- Keywords
- spatial, nonparametric
Usage
Ginhom(X, lambda = NULL, lmin = NULL, ...,
sigma = NULL, varcov = NULL,
r = NULL, breaks = NULL, ratio = FALSE,
update = TRUE, warn.bias=TRUE, savelambda=FALSE)
Arguments
- X
The observed data point pattern, from which an estimate of the inhomogeneous \(G\) function will be computed. An object of class
"ppp"
or in a format recognised byas.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 afunction(x,y)
which can be evaluated to give the intensity value at any location.- lmin
Optional. The minimum possible value of the intensity over the spatial domain. A positive numerical value.
- sigma,varcov
Optional arguments passed to
density.ppp
to control the smoothing bandwidth, whenlambda
is estimated by kernel smoothing.- …
Extra arguments passed to
as.mask
to control the pixel resolution, or passed todensity.ppp
to control the smoothing bandwidth.- r
vector of values for the argument \(r\) at which the inhomogeneous \(K\) function should be evaluated. Not normally given by the user; there is a sensible default.
- breaks
This argument is for internal use only.
- ratio
Logical. If
TRUE
, the numerator and denominator of the estimate will also be saved, for use in analysing replicated point patterns.- update
Logical. If
lambda
is a fitted model (class"ppm"
or"kppm"
) andupdate=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 fitting it toX
.- warn.bias
Logical value specifying whether to issue a warning when the inhomogeneity correction factor takes extreme values, which can often lead to biased results. This usually occurs when insufficient smoothing is used to estimate the intensity.
- savelambda
Logical value specifying whether to save the values of
lmin
andlambda
as attributes of the result.
Details
This command computes estimates of the
inhomogeneous \(G\)-function (van Lieshout, 2010)
of a point pattern. It is the counterpart, for inhomogeneous
spatial point patterns, of the nearest-neighbour distance
distribution function \(G\)
for homogeneous point patterns computed by Gest
.
The argument X
should be a point pattern
(object of class "ppp"
).
The inhomogeneous \(G\) function is computed using the border correction, equation (7) in Van Lieshout (2010).
The argument lambda
should supply the
(estimated) values of the intensity function \(\lambda\)
of the point process. It may be either
- a numeric vector
containing the values of the intensity function at the points of the pattern
X
.- a pixel image
(object of class
"im"
) assumed to contain the values of the intensity function at all locations in the window.- a fitted point process model
(object of class
"ppm"
or"kppm"
) whose fitted trend can be used as the fitted intensity. (Ifupdate=TRUE
the model will first be refitted to the dataX
before the trend is computed.)- a function
which can be evaluated to give values of the intensity at any locations.
- omitted:
if
lambda
is omitted, then it will be estimated using a `leave-one-out' kernel smoother.
If lambda
is a numeric vector, then its length should
be equal to the number of points in the pattern X
.
The value lambda[i]
is assumed to be the
the (estimated) value of the intensity
\(\lambda(x_i)\) for
the point \(x_i\) of the pattern \(X\).
Each value must be a positive number; NA
's are not allowed.
If lambda
is a pixel image, the domain of the image should
cover the entire window of the point pattern. If it does not (which
may occur near the boundary because of discretisation error),
then the missing pixel values
will be obtained by applying a Gaussian blur to lambda
using
blur
, then looking up the values of this blurred image
for the missing locations.
(A warning will be issued in this case.)
If lambda
is a function, then it will be evaluated in the
form lambda(x,y)
where x
and y
are vectors
of coordinates of the points of X
. It should return a numeric
vector with length equal to the number of points in X
.
If lambda
is omitted, then it will be estimated using
a `leave-one-out' kernel smoother.
The estimate lambda[i]
for the
point X[i]
is computed by removing X[i]
from the
point pattern, applying kernel smoothing to the remaining points using
density.ppp
, and evaluating the smoothed intensity
at the point X[i]
. The smoothing kernel bandwidth is controlled
by the arguments sigma
and varcov
, which are passed to
density.ppp
along with any extra arguments.
Value
An object of class "fv"
, see fv.object
,
which can be plotted directly using plot.fv
.
References
Van Lieshout, M.N.M. and Baddeley, A.J. (1996) A nonparametric measure of spatial interaction in point patterns. Statistica Neerlandica 50, 344--361.
Van Lieshout, M.N.M. (2010) A J-function for inhomogeneous point processes. Statistica Neerlandica 65, 183--201.
See Also
Examples
# NOT RUN {
# }
# NOT RUN {
plot(Ginhom(swedishpines, sigma=bw.diggle, adjust=2))
# }
# NOT RUN {
plot(Ginhom(swedishpines, sigma=10))
# }