Computes the influence measure for a fitted spatial point process model.

```
# S3 method for ppm
influence(model, …,
drop = FALSE, iScore=NULL, iHessian=NULL, iArgs=NULL)
```

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`

,
`iHessian`

if required.

An object of class `"influence.ppm"`

.

Given a fitted spatial point process model `model`

,
this function computes the influence measure
described in Baddeley, Chang and Song (2013)
and Baddeley, Rubak and Turner (2019).

The function `influence`

is generic,
and `influence.ppm`

is the method for objects of class
`"ppm"`

representing point process models.

The influence of a point process model is a value attached to each data point
(i.e. each point of the point pattern to which the `model`

was fitted).
The influence value \(s(x_i)\) at a data point
\(x_i\) represents the change in the maximised log (pseudo)likelihood
that occurs when the point \(x_i\) is deleted.
A relatively large value of \(s(x_i)\) indicates a
data point with a large influence on the fitted model.

If the point process model trend has irregular parameters that were
fitted (using `ippm`

)
then the influence 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 `influence.ppm`

is
an object of class `"influence.ppm"`

. It can be printed and plotted.
It can be converted to a marked
point pattern by `as.ppp`

(see `as.ppp.influence.ppm`

).
There are also methods for `[`

,
`as.owin`

, `domain`

,
`shift`

, `integral`

and `Smooth`

.

Baddeley, A. and 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.

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