# fitted.ppm

0th

Percentile

##### Fitted Conditional Intensity for Point Process Model

Given a point process model fitted to a point pattern, compute the fitted conditional intensity of the model at the points of the pattern, or at the points of the quadrature scheme used to fit the model.

Keywords
models, methods, spatial
##### Usage
## S3 method for class 'ppm':
fitted(object, \dots, type="lambda", dataonly=FALSE)
##### Arguments
object
The fitted point process model (an object of class "ppm")
...
Ignored.
type
String (partially matched) indicating whether the fitted value is the conditional intensity ("lambda") or the trend ("trend").
dataonly
Logical. If TRUE, then values will only be computed at the points of the data point pattern. If FALSE, then values will be computed at all the points of the quadrature scheme used to fit the model, including the point
##### Details

The argument object must be a fitted point process model (object of class "ppm"). Such objects are produced by the model-fitting algorithm ppm).

This function evaluates the conditional intensity $\hat\lambda(u, x)$ or spatial trend $\hat b(u)$ of the fitted point process model for certain locations $u$, where x is the original point pattern dataset to which the model was fitted.

The locations $u$ at which the fitted conditional intensity/trend is evaluated, are the points of the quadrature scheme used to fit the model in ppm. They include the data points (the points of the original point pattern dataset x) and other dummy'' points in the window of observation.

Use predict.ppm to compute the fitted conditional intensity at other locations or with other values of the explanatory variables.

##### Value

• A vector containing the values of the fitted conditional intensity or (if type="trend") the fitted spatial trend. Entries in this vector correspond to the quadrature points (data or dummy 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 (with discussion). Journal of the Royal Statistical Society, Series B 67, 617--666.

ppm.object, ppm, predict.ppm

• fitted.ppm
##### Examples
data(cells)
str <- ppm(cells, ~x, Strauss(r=0.15), rbord=0.15)
lambda <- fitted(str)

# extract quadrature points in corresponding order
plot(quadmarked)