R: Fitted Conditional Intensity for Point Process Model

fitted.ppm {spatstat.core} | R Documentation

## Fitted Conditional Intensity for Point Process Model

### Description

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

### Usage

      ## S3 method for class 'ppm'
    fitted(object, ..., type="lambda",
                           dataonly=FALSE, new.coef=NULL, leaveoneout=FALSE,
    		       drop=FALSE, check=TRUE, repair=TRUE,
    		       ignore.hardcore=FALSE, dropcoef=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 `"cif"`) or the first order trend (`"trend"`) or the logarithm of conditional intensity (`"link"`).
`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 points of the data point pattern.
`new.coef` | Numeric vector of parameter values to replace the fitted model parameters `coef(object)`.
`leaveoneout` | Logical. If `TRUE` the fitted value at each data point will be computed using a leave-one-out method. See Details.
`drop` | Logical value determining whether to delete quadrature points that were not used to fit the model.
`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 computed, set `check=TRUE`.
`repair` | Logical value indicating whether to repair the internal format of `object`, if it is found to be damaged.
`ignore.hardcore` | Advanced use only. Logical value specifying whether to compute only the finite part of the interaction potential (effectively removing any hard core interaction terms).
`dropcoef` | Internal use only.

### 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 lambdahat(u,x) or spatial trend bhat(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.

If `leaveoneout=TRUE`, fitted values will be computed for the data points only, using a ‘leave-one-out’ rule: the fitted value at `X[i]` is effectively computed by deleting this point from the data and re-fitting the model to the reduced pattern `X[-i]`, then predicting the value at `X[i]`. (Instead of literally performing this calculation, we apply a Taylor approximation using the influence function computed in `dfbetas.ppm`.

The argument `drop` is explained in `quad.ppm`.

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, fitted spatial trend, or logarithm 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))`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

### 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.

### See Also

`ppm.object`, `ppm`, `predict.ppm`

### Examples

        str <- ppm(cells ~x, Strauss(r=0.1))
        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)

        if(!interactive()) str <- ppm(cells ~ x)

        lambdaX <- fitted(str, leaveoneout=TRUE)

[Package spatstat.core version 2.4-4 Index]