leverage.ppm {spatstat} | R Documentation |
Computes the leverage measure for a fitted spatial point process model.
leverage(model, ...) ## S3 method for class 'ppm' leverage(model, ..., drop = FALSE, iScore=NULL, iHessian=NULL, iArgs=list())
model |
Fitted point process model (object of class |
... |
Ignored. |
drop |
Logical. Whether to include ( |
iScore,iHessian |
Components of the score vector and Hessian matrix for the irregular parameters, if required. See Details. |
iArgs |
List of extra arguments for the functions |
The function 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 (2011).
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
).
An object of class "leverage.ppm"
that can be plotted
by plot.leverage.ppm
.
Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/
Baddeley, A. and Chang, Y.M. and Song, Y. (2011) Leverage and influence diagnostics for spatial point process models. Scandinavian Journal of Statistics, in press.
influence.ppm
,
dfbetas.ppm
,
plot.leverage.ppm
X <- rpoispp(function(x,y) { exp(3+3*x) }) fit <- ppm(X, ~x+y) plot(leverage(fit))