# residuals.ppm

0th

Percentile

##### Residuals for Fitted Point Process Model

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

Keywords
models, methods, spatial
##### 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.

diagnose.ppm, ppm.object, ppm

##### Aliases
• residuals.ppm
##### 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
plot(quadmarked)