# 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 ppm
leverage(model, …,
drop = FALSE, iScore=NULL, iHessian=NULL, iArgs=NULL)

##### Arguments

- model
Fitted point process model (object of class

`"ppm"`

).- …
Ignored, except for the arguments

`dimyx`

and`eps`

which are passed to`as.mask`

to control the spatial resolution of the result.- 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`

,`iHessian`

if 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)
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`

.

##### Value

An object of class `"leverage.ppm"`

.

##### 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.

Baddeley, A., Rubak, E. and Turner, R. (2019)
Leverage and influence diagnostics for Gibbs spatial point processes.
*Spatial Statistics* **29**, 15--48.

##### See Also

`influence.ppm`

,
`dfbetas.ppm`

,
`ppmInfluence`

,
`plot.leverage.ppm`

`as.function.leverage.ppm`

##### Examples

```
# NOT RUN {
X <- rpoispp(function(x,y) { exp(3+3*x) })
fit <- ppm(X ~x+y)
plot(le <- leverage(fit))
mean(le)
# }
```

*Documentation reproduced from package spatstat, version 1.61-0, License: GPL (>= 2)*