influence.ppm

0th

Percentile

Influence Measure for Spatial Point Process Model

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

Keywords
models, spatial
Usage
## S3 method for class 'ppm':
influence(model, ..., drop = FALSE, iScore=NULL, iHessian=NULL, iArgs=list())
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 Rfunctions 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 Rfunctions 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.

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.

leverage.ppm, dfbetas.ppm, plot.influence.ppm

Aliases
• influence.ppm
Examples
X <- rpoispp(function(x,y) { exp(3+3*x) })
fit <- ppm(X, ~x+y)
plot(influence(fit))
Documentation reproduced from package spatstat, version 1.36-0, License: GPL (>= 2)

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