# dfbetas.ppm

##### Parameter Influence Measure

Computes the deletion influence measure for each parameter in a fitted point process model.

##### Usage

```
# S3 method for ppm
dfbetas(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 image of the density component.- 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`

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

This is a method for the generic function `dfbetas`

.

The influence measure for each parameter \(\theta\) is a
signed measure in two-dimensional space. It consists of a discrete
mass on each data point (i.e. each point in the point pattern to which
the `model`

was originally fitted) and a continuous density at
all locations. The mass at a data point represents the change in the
fitted value of the parameter \(\theta\) that would occur
if this data point were to be deleted.
The density at other non-data locations represents the
effect (on the fitted value of \(\theta\))
of deleting these locations (and their associated covariate values)
from the input to the fitting procedure.

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.

##### Value

An object of class `"msr"`

representing a signed or vector-valued
measure. This object can be printed and plotted.

##### 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.

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

##### See Also

`leverage.ppm`

,
`influence.ppm`

,
`ppmInfluence`

.

See `msr`

for information on how to use a measure.

##### Examples

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

*Documentation reproduced from package spatstat, version 1.63-2, License: GPL (>= 2)*