Gcross.inhom {spatstat.explore} | R Documentation |
Inhomogeneous Multitype G Cross Function
Description
For a multitype point pattern,
estimate the inhomogeneous version of the cross function,
which is the distribution of the distance
from a point of type
to the nearest point of type
,
adjusted for spatially varying intensity.
Usage
Gcross.inhom(X, i, j,
lambda = NULL, lambdaI = NULL, lambdaJ = NULL,
lambdamin = NULL,
...,
r = NULL,
ReferenceMeasureMarkSetI = NULL,
ratio = FALSE)
Arguments
X |
The observed point pattern,
from which an estimate of the inhomogeneous cross type |
i |
The type (mark value)
of the points in |
j |
The type (mark value)
of the points in |
lambda |
Optional.
Values of the estimated intensity of the point process.
Either a pixel image (object of class |
lambdaI |
Optional.
Values of the estimated intensity of the sub-process of
points of type |
lambdaJ |
Optional.
Values of the the estimated intensity of the sub-process of
points of type |
lambdamin |
Optional. The minimum possible value of the intensity over the spatial domain. A positive numerical value. |
... |
Extra arguments passed to |
r |
vector of values for the argument |
ReferenceMeasureMarkSetI |
Optional. The total measure of the mark set. A positive number. |
ratio |
Logical value indicating whether to save ratio information. |
Details
This is a generalisation of the function Gcross
to include an adjustment for spatially inhomogeneous intensity,
in a manner similar to the function Ginhom
.
The argument lambdaI
supplies the values
of the intensity of the sub-process of points of type i
.
It may be either
- a pixel image
(object of class
"im"
) which gives the values of the typei
intensity at all locations in the window containingX
;- a numeric vector
containing the values of the type
i
intensity evaluated only at the data points of typei
. The length of this vector must equal the number of typei
points inX
.- a function
-
of the form
function(x,y)
which can be evaluated to give values of the intensity at any locations. - a fitted point process model
-
(object of class
"ppm"
,"kppm"
or"dppm"
) 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.) - omitted:
-
if
lambdaI
is omitted then it will be estimated using a leave-one-out kernel smoother.
If lambdaI
is omitted, then it will be estimated using
a ‘leave-one-out’ kernel smoother.
Similarly the argument lambdaJ
should contain
estimated values of the intensity of the points of type .
It may be either a pixel image, a numeric vector of length equal
to the number of points in
X
, a function, or omitted.
The argument r
is the vector of values for the
distance at which
should be evaluated.
The values of
must be increasing nonnegative numbers
and the maximum
value must not exceed the radius of the
largest disc contained in the window.
Value
An object of class "fv"
(see fv.object
)
containing estimates of the inhomogeneous cross type function.
Warnings
The argument i
is interpreted as
a level of the factor X$marks
. It is converted to a character
string if it is not already a character string.
The value i=1
does not
refer to the first level of the factor.
Author(s)
Adrian Baddeley Adrian.Baddeley@curtin.edu.au.
References
Cronie, O. and Van Lieshout, M.N.M. (2015) Summary statistics for inhomogeneous marked point processes. Annals of the Institute of Statistical Mathematics DOI: 10.1007/s10463-015-0515-z
See Also
Gcross
,
Ginhom
,
Gcross.inhom
,
Gmulti.inhom
.
Examples
X <- rescale(amacrine)
if(interactive() && require(spatstat.model)) {
## how to do it normally
mod <- ppm(X ~ marks * x)
lam <- fitted(mod, dataonly=TRUE)
lmin <- min(predict(mod)[["off"]]) * 0.9
} else {
## for package testing
lam <- intensity(X)[as.integer(marks(X))]
lmin <- intensity(X)[2] * 0.9
}
GC <- Gcross.inhom(X, "on", "off", lambda=lam, lambdamin=lmin)