# residuals.ppm

##### Residuals for Fitted Point Process Model

Given a point process model fitted to a point pattern, compute residuals.

##### Usage

```
## S3 method for class 'ppm':
residuals(object, type="raw", \dots, check=TRUE, drop=FALSE,
fittedvalues=fitted.ppm(object, check=check, drop=drop))
```

##### Arguments

- object
- The fitted point process model (an object of class
`"ppm"`

) for which residuals should be calculated. - type
- String indicating the type of residuals to be calculated.
Current options are
`"raw"`

,`"inverse"`

,`"pearson"`

and`"score"`

. A partial match is adequate. - ...
- Ignored.
- check
- Logical value indicating whether to check the internal format
of
`object`

. If there is any possibility that this object has been restored from a dump file, or has otherwise lost track of the environment where it was originally compu - drop
- Logical value determining whether to delete quadrature points
that were not used to fit the model. See
`quad.ppm`

for explanation. - fittedvalues
- Vector of fitted values for the conditional intensity at the quadrature points, from which the residuals will be computed. For expert use only.

##### Details

This function computes several kinds of residuals for the fit of
a point process model to a spatial point pattern dataset
(Baddeley et al, 2005).
Use `diagnose.ppm`

to produce diagnostic plots
based on these residuals.

The argument `object`

must be a fitted point process model
(object of class `"ppm"`

). Such objects are produced by the maximum
pseudolikelihood fitting algorithm `ppm`

).
This fitted model object contains complete
information about the original data pattern.

Residuals are attached both to the data points and to some
other points in the window of observation (namely, to the dummy
points of the quadrature scheme used to fit the model).
If the fitted model is correct, then the sum of the
residuals over all (data and dummy) points in a spatial region $B$
has mean zero. For further explanation, see Baddeley et al (2005).
The type of residual
is chosen by the argument `type`

. Current options are

[object Object],[object Object],[object Object],[object Object]

Use `diagnose.ppm`

to produce diagnostic plots
based on these residuals.

##### Value

- If
`type`

is`"raw"`

,`"inverse"`

or`"pearson"`

: a vector containing the discretised residuals. Entries in this vector correspond to the quadrature points (data or dummy points) used to fit the model. If`type = "score"`

: a matrix whose columns are components of the discretised score residuals. Rows in this matrix correspond to the quadrature points used to fit the model. The quadrature points can be extracted from`object`

by`union.quad(quad.ppm(object))`

.

##### References

Baddeley, A., Turner, R., Moller, J. and Hazelton, M. (2005)
Residual analysis for spatial point processes.
*Journal of the Royal Statistical Society, Series B*
**67**, 617--666.

Baddeley, A., Moller, J. and Pakes, A.G. (2008)
Properties of residuals for spatial point processes.
*Annals of the Institute of Statistical Mathematics*
**60**, 627--649.

##### See Also

##### Examples

```
data(cells)
fit <- ppm(cells, ~x, Strauss(r=0.15))
rp <- residuals.ppm(fit, type="pe")
sum(rp) # should be close to 0
# extract quadrature points to which the residuals correspond
quadpoints <- union.quad(quad.ppm(fit))
# plot residuals as marks attached to the quadrature points
quadmarked <- setmarks(quadpoints, rp)
plot(quadmarked)
```

*Documentation reproduced from package spatstat, version 1.21-0, License: GPL (>= 2)*