# influence.ppm

##### Influence Measure for Spatial Point Process Model

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

##### Usage

```
# S3 method for ppm
influence(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`

,`iHessian`

if required.

##### Details

Given a fitted spatial point process model `model`

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

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 plotted
(by `plot.influence.ppm`

), or converted to a marked
point pattern by `as.ppp`

(see `as.ppp.influence.ppm`

).

##### Value

An object of class `"influence.ppm"`

that can be plotted
(by `plot.influence.ppm`

). There are also methods
for `print`

, `[`

, `as.ppp`

and `as.owin`

.

##### References

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.

##### See Also

##### Examples

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

*Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)*