R: Influence Measure for Spatial Point Process Model

influence.ppm {spatstat} | R Documentation

## Influence Measure for Spatial Point Process Model

### Description

Computes the influence measure for a fitted spatial point process model.

### Usage

    ## S3 method for class 'ppm'
    influence(model, ..., drop = FALSE, iScore=NULL, iHessian=NULL, iArgs=NULL)

### Arguments

`model` | Fitted point process model (object of class `"ppm"`).
`...` | Ignored.
`drop` | Logical. Whether to include (`drop=FALSE`) or exclude (`drop=TRUE`) contributions from quadrature points that were not used to fit the model.
`iScore,iHessian` | Components of the score vector and Hessian matrix for the irregular parameters, if required. See Details.
`iArgs` | List of extra arguments for the functions `iScore`, `iHessian` if required.

### Details

Given a fitted spatial point process model `model`, this function computes the influence measure described in Baddeley, Chang and Song (2013).

The function `influence` is generic, and `influence.ppm` is the method for objects of class `"ppm"` representing point process models.

The influence of a point process model is a value attached to each data point (i.e. each point of the point pattern to which the `model` was fitted). The influence value s(x[i]) at a data point x[i] represents the change in the maximised log (pseudo)likelihood that occurs when the point x[i] is deleted. A relatively large value of s(x[i]) indicates a data point with a large influence on the fitted model.

If the point process model trend has irregular parameters that were fitted (using `ippm`) then the influence calculation requires the first and second derivatives of the log trend with respect to the irregular parameters. The argument `iScore` should be a list, with one entry for each irregular parameter, of R functions that compute the partial derivatives of the log trend (i.e. log intensity or log conditional intensity) with respect to each irregular parameter. The argument `iHessian` should be a list, with p^2 entries where p is the number of irregular parameters, of R functions that compute the second order partial derivatives of the log trend with respect to each pair of irregular parameters.

The result of `influence.ppm` is an object of class `"influence.ppm"`. It can be plotted (by `plot.influence.ppm`), or converted to a marked point pattern by `as.ppp` (see `as.ppp.influence.ppm`).

### Value

An object of class `"influence.ppm"` that can be plotted (by `plot.influence.ppm`). There are also methods for `print`, `[`, `as.ppp` and `as.owin`.

### 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. and Chang, Y.M. and Song, Y. (2013) Leverage and influence diagnostics for spatial point process models. Scandinavian Journal of Statistics 40, 86–104.

### See Also

`leverage.ppm`, `dfbetas.ppm`, `ppmInfluence`, `plot.influence.ppm`

### Examples

       X <- rpoispp(function(x,y) { exp(3+3*x) })
       fit <- ppm(X ~x+y)
       plot(influence(fit))

[Package spatstat version 1.54-0 Index]