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For a multitype point pattern,
estimate the inhomogeneous version of the dot
Gdot.inhom(X, i,
lambdaI = NULL, lambdadot = NULL, lambdamin = NULL,
...,
r = NULL, ReferenceMeasureMarkSetI = NULL, ratio = FALSE)
An object of class "fv"
(see fv.object
)
containing estimates of the inhomogeneous dot type
The observed point pattern,
from which an estimate of the inhomogeneous dot type
The type (mark value)
of the points in X
from which distances are measured.
A character string (or something that will be converted to a
character string).
Defaults to the first level of marks(X)
.
Optional.
Values of the estimated intensity of the sub-process of
points of type i
.
Either a pixel image (object of class "im"
),
a numeric vector containing the intensity values
at each of the type i
points in X
,
a fitted point process model
(object of class "ppm"
or "kppm"
or "dppm"
),
or a function(x,y)
which
can be evaluated to give the intensity value at any location.
Optional.
Values of the estimated intensity of the entire point process,
Either a pixel image (object of class "im"
),
a numeric vector containing the intensity values at each of the
points in X
, a fitted point process model
(object of class "ppm"
or "kppm"
or "dppm"
),
or a function(x,y)
which
can be evaluated to give the intensity value at any location.
Optional. The minimum possible value of the intensity over the spatial domain. A positive numerical value.
Ignored.
vector of values for the argument
Optional. The total measure of the mark set. A positive number.
Logical value indicating whether to save ratio information.
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.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner rolfturner@posteo.net and Ege Rubak rubak@math.aau.dk
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
(object of class "im"
) which
gives the values of the type i
intensity
at all locations in the window containing X
;
containing the values of the
type i
intensity evaluated only
at the data points of type i
. The length of this vector
must equal the number of type i
points in X
.
of the form function(x,y)
which can be evaluated to give values of the intensity at
any locations.
(object of class "ppm"
, "kppm"
or "dppm"
)
whose fitted trend can be used as the fitted intensity.
(If update=TRUE
the model will first be refitted to the
data X
before the trend is computed.)
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
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
Gdot
,
Ginhom
,
Gcross.inhom
,
Gmulti.inhom
.
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)
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