fitted.ppm: Fitted Conditional Intensity for Point Process Model

Description

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.

Usage

fitted.ppm(object, ...)

Arguments

object

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

...

Ignored.

Value

A vector containing the values of the fitted conditional intensity. 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)).

Details

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

This function evaluates the conditional intensity $\hat\lambda(u, x)$ 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 is evaluated, are the points of the quadrature scheme used to fit the model in mpl. 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.

References

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

Examples

Run this code

require(spatstat)
    data(cells)
    str <- mpl(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)

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