leverage.ppm
Leverage Measure for Spatial Point Process Model
Computes the leverage measure for a fitted spatial point process model.
Usage
leverage(model, ...)
## S3 method for class 'ppm':
leverage(model, ..., drop = FALSE, iScore=NULL, iHessian=NULL, iArgs=NULL)Arguments
- model
- Fitted point process model (object of class
"ppm"). - ...
- Ignored.
- drop
- Logical. Whether to include (
drop=FALSE) or exclude (drop=TRUE) contributions from quadrature points that were not used to fit the model. - 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
iScore,iHessianif required.
Details
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).
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 Rfunctions 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 Rfunctions 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).
Value
- An object of class
"leverage.ppm"that can be plotted (byplot.leverage.ppm). There are also methods forprint,[,as.imandas.owin.
References
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.
See Also
Examples
X <- rpoispp(function(x,y) { exp(3+3*x) })
fit <- ppm(X, ~x+y)
plot(leverage(fit))