Gdot.inhom {spatstat.explore} | R Documentation |
Inhomogeneous Multitype G Dot Function
Description
For a multitype point pattern,
estimate the inhomogeneous version of the dot G
function,
which is the distribution of the distance
from a point of type i
to the nearest other point of any type,
adjusted for spatially varying intensity.
Usage
Gdot.inhom(X, i,
lambdaI = NULL, lambdadot = NULL, lambdamin = NULL,
...,
r = NULL, ReferenceMeasureMarkSetI = NULL, ratio = FALSE)
Arguments
X |
The observed point pattern,
from which an estimate of the inhomogeneous dot type |
i |
The type (mark value)
of the points in |
lambdaI |
Optional.
Values of the estimated intensity of the sub-process of
points of type |
lambdadot |
Optional.
Values of the estimated intensity of the entire point process,
Either a pixel image (object of class |
lambdamin |
Optional. The minimum possible value of the intensity over the spatial domain. A positive numerical value. |
... |
Ignored. |
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 Gdot
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 lambdadot
should contain
estimated values of the intensity of the entire point process.
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 r
at which G_{i\bullet}(r)
should be evaluated.
The values of r
must be increasing nonnegative numbers
and the maximum r
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 dot type G
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, Rolf Turner rolfturner@posteo.net and Ege Rubak rubak@math.aau.dk
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
Gdot
,
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
}
lamI <- lam[marks(X) == "on"]
GD <- Gdot.inhom(X, "on", lambdaI=lamI, lambdadot=lam, lambdamin=lmin)