Leverage Measure for Spatial Point Process Model
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=NULL)model |
Fitted point process model (object of class |
... |
Ignored, except for the arguments |
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 (2013)
and Baddeley, Rubak and Turner (2019).
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 conditional intensity 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 printed or plotted.
It can be converted to a pixel image
by as.im (see as.im.leverage.ppm).
There are also methods for contour, persp,
[, as.function,
as.owin, domain, Smooth,
integral, and mean.
An object of class "leverage.ppm".
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
Baddeley, A., Chang, Y.M. and Song, Y. (2013) Leverage and influence diagnostics for spatial point process models. Scandinavian Journal of Statistics 40, 86–104.
Baddeley, A., Rubak, E. and Turner, R. (2019) Leverage and influence diagnostics for Gibbs spatial point processes. Spatial Statistics 29, 15–48.
X <- rpoispp(function(x,y) { exp(3+3*x) })
fit <- ppm(X ~x+y)
plot(le <- leverage(fit))
mean(le)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.