# fitted.ppm

##### 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 quadrature scheme used to fit the model.

- Keywords
- spatial

##### Usage

`fitted.ppm(object, ..., type="lambda")`

##### 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"`

).

##### 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., Moller, J. and Turner, R. (2004) Residuals for spatial point processes. In preparation.

##### See Also

##### Examples

```
data(cells)
str <- ppm(cells, ~x, Strauss(r=0.15), rbord=0.15)
lambda <- fitted(str)
# extract quadrature points in corresponding order
quadpoints <- union.quad(quad.ppm(str))
# plot conditional intensity values
# as circles centred on the quadrature points
quadmarked <- setmarks(quadpoints, lambda)
plot(quadmarked)
```

*Documentation reproduced from package spatstat, version 1.5-5, License: GPL version 2 or newer*