Computes an estimate of the inhomogeneous pair correlation function based on Euclidean distances, for a point pattern on a linear network.
linearpcfEuclidInhom(X, lambda = NULL, r = NULL, ...,
normalise = TRUE, normpower = 2,
update = TRUE, leaveoneout = TRUE,
sigma=NULL, adjust.sigma=1, bw="nrd0", adjust.bw=1)Function value table (object of class "fv").
This command computes the inhomogeneous version of the pair correlation function based on Euclidean distances, for a point pattern on a linear network.
This is different from the inhomogeneous pair correlation function based on
shortest-path distances,
which is computed by linearpcfinhom.
The inhomogeneous pair correlation function based on Euclidean distances is defined in equation (30) of Rakshit, Nair and Baddeley (2017). Estimation is performed as described in equation (34) of Rakshit, Nair and Baddeley (2017).
The argument lambda should provide estimated values
of the intensity of the point process at each point of X.
If lambda=NULL, the intensity will be estimated by kernel
smoothing by calling density.lpp with the smoothing
bandwidth sigma, and with any other relevant arguments
that might be present in .... A leave-one-out kernel estimate
will be computed if leaveoneout=TRUE.
If lambda is given, then it
may be a numeric vector (of length equal to
the number of points in X), or a function(x,y) that will be
evaluated at the points of X to yield numeric values,
or a pixel image (object of class "im") or a fitted point
process model (object of class "ppm" or "lppm").
If lambda 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.
The intensity at data points will be computed
by fitted.lppm or fitted.ppm.
A leave-one-out estimate will be computed if leaveoneout=TRUE
and update=TRUE.
If normalise=TRUE (the default), then the estimate
is multiplied by \(c^{\mbox{normpower}}\) where
\(
c = \mbox{length}(L)/\sum (1/\lambda(x_i)).
\)
This rescaling reduces the variability and bias of the estimate
in small samples and in cases of very strong inhomogeneity.
The default value of normpower is 1 (for consistency with
previous versions of spatstat)
but the most sensible value is 2, which would correspond to rescaling
the lambda values so that
\(
\sum (1/\lambda(x_i)) = \mbox{area}(W).
\)
Rakshit. S., Nair, G. and Baddeley, A. (2017) Second-order analysis of point patterns on a network using any distance metric. Spatial Statistics 22 (1) 129--154.
linearKEuclidInhom, linearpcfEuclid.
See linearpcfinhom for the corresponding function
based on shortest-path distances.
X <- rpoislpp(5, simplenet)
fit <- lppm(X ~x)
g <- linearpcfEuclidInhom(X, lambda=fit)
plot(g)
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