leverage(model, ...)
"leverage"(model, ..., drop = FALSE, iScore=NULL, iHessian=NULL, iArgs=NULL)"ppm").
drop=FALSE) or
exclude (drop=TRUE) contributions from quadrature
points that were not used to fit the model.
iScore,
iHessian if required.
"leverage.ppm" that can be plotted
(by plot.leverage.ppm). There are also methods
for print, [, as.im and as.owin.
leverage is generic, and
leverage.ppm is the method for objects of class "ppm".
Given a fitted spatial point process model model,
the function leverage.ppm computes the leverage of the model,
described in Baddeley, Chang and Song (2013).
The leverage of a spatial point process model
is a function of spatial location, and is typically
displayed as a colour pixel image.
The leverage value $h(u)$ at a spatial location $u$ represents the
change in the fitted trend of the fitted point process model that would have
occurred if a data point were to have occurred at the location $u$.
A relatively large value of $h()$ indicates a
part of the space where the data have a potentially
strong effect on the fitted model (specifically, a strong effect
on the intensity or trend of the fitted model) due to the values
of the covariates.
If the point process model trend has irregular parameters that were
fitted (using ippm)
then the leverage calculation requires the first and second
derivatives of the log trend with respect to the irregular parameters.
The argument iScore should be a list,
with one entry for each irregular parameter, of R functions that compute the
partial derivatives of the log trend (i.e. log intensity or
log conditional intensity) with respect to each irregular
parameter. The argument iHessian should be a list,
with $p^2$ entries where $p$ is the number of irregular
parameters, of R functions that compute the second order
partial derivatives of the log trend with respect to each
pair of irregular parameters. The result of leverage.ppm is an object of
class "leverage.ppm". It can be plotted
(by plot.leverage.ppm) or converted to a pixel
image by as.im (see as.im.leverage.ppm).
influence.ppm,
dfbetas.ppm,
ppmInfluence,
plot.leverage.ppm
X <- rpoispp(function(x,y) { exp(3+3*x) })
fit <- ppm(X ~x+y)
plot(leverage(fit))
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