linearpcfdot.inhom
Inhomogeneous Multitype Pair Correlation Function (Dot-type) for Linear Point Pattern
For a multitype point pattern on a linear network, estimate the inhomogeneous multitype pair correlation function from points of type \(i\) to points of any type.
- Keywords
- spatial, nonparametric
Usage
linearpcfdot.inhom(X, i, lambdaI, lambdadot, r=NULL, …,
correction="Ang", normalise=TRUE)
Arguments
- X
The observed point pattern, from which an estimate of the \(i\)-to-any pair correlation function \(g_{i\bullet}(r)\) will be computed. An object of class
"lpp"
which must be a multitype point pattern (a marked point pattern whose marks are a factor).- i
Number or character string identifying the type (mark value) of the points in
X
from which distances are measured. Defaults to the first level ofmarks(X)
.- lambdaI
Intensity values for the points of type
i
. Either a numeric vector, afunction
, a pixel image (object of class"im"
or"linim"
) or a fitted point process model (object of class"ppm"
or"lppm"
).- lambdadot
Intensity values for all points of
X
. Either a numeric vector, afunction
, a pixel image (object of class"im"
or"linim"
) or a fitted point process model (object of class"ppm"
or"lppm"
).- r
numeric vector. The values of the argument \(r\) at which the function \(g_{i\bullet}(r)\) should be evaluated. There is a sensible default. First-time users are strongly advised not to specify this argument. See below for important conditions on \(r\).
- correction
Geometry correction. Either
"none"
or"Ang"
. See Details.- …
Arguments passed to
density.default
to control the kernel smoothing.- normalise
Logical. If
TRUE
(the default), the denominator of the estimator is data-dependent (equal to the sum of the reciprocal intensities at the points of typei
), which reduces the sampling variability. IfFALSE
, the denominator is the length of the network.
Details
This is a counterpart of the function pcfdot.inhom
for a point pattern on a linear network (object of class "lpp"
).
The argument i
will be interpreted as
levels of the factor marks(X)
.
If i
is missing, it defaults to the first
level of the marks factor.
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.
If lambdaI
or lambdadot
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
.
Value
An object of class "fv"
(see fv.object
).
Warnings
The argument i
is interpreted as a
level of the factor marks(X)
. Beware of the usual
trap with factors: numerical values are not
interpreted in the same way as character values.
References
Baddeley, A, Jammalamadaka, A. and Nair, G. (to appear) Multitype point process analysis of spines on the dendrite network of a neuron. Applied Statistics (Journal of the Royal Statistical Society, Series C), 63, 673--694.
See Also
Examples
# NOT RUN {
lam <- table(marks(chicago))/(summary(chicago)$totlength)
lamI <- function(x,y,const=lam[["assault"]]){ rep(const, length(x)) }
lam. <- function(x,y,const=sum(lam)){ rep(const, length(x)) }
g <- linearpcfdot.inhom(chicago, "assault", lamI, lam.)
# }
# NOT RUN {
fit <- lppm(chicago, ~marks + x)
linearpcfdot.inhom(chicago, "assault", fit, fit)
# }