residuals.ppm: Residuals for Fitted Point Process Model

Description

Given a point process model fitted to a point pattern, compute residuals.

Usage

## S3 method for class 'ppm':
residuals(object, type="raw", \dots, check=TRUE, drop=FALSE,
                fittedvalues=fitted.ppm(object, check=check, drop=drop))

Arguments

object

The fitted point process model (an object of class "ppm") for which residuals should be calculated.

type

String indicating the type of residuals to be calculated. Current options are "raw", "inverse", "pearson" and "score". A partial match is adequate.

...

Ignored.

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 compu

drop

Logical value determining whether to delete quadrature points that were not used to fit the model. See quad.ppm for explanation.

fittedvalues

Vector of fitted values for the conditional intensity at the quadrature points, from which the residuals will be computed. For expert use only.

Value

An object of class "msr" representing a signed measure or vector-valued measure (see msr). This object can be plotted.

Details

This function computes several kinds of residuals for the fit of a point process model to a spatial point pattern dataset (Baddeley et al, 2005). Use plot.msr to plot the residuals directly, or diagnose.ppm to produce diagnostic plots based on these residuals.

The argument object must be a fitted point process model (object of class "ppm"). Such objects are produced by the maximum pseudolikelihood fitting algorithm ppm). This fitted model object contains complete information about the original data pattern.

Residuals are attached both to the data points and to some other points in the window of observation (namely, to the dummy points of the quadrature scheme used to fit the model). If the fitted model is correct, then the sum of the residuals over all (data and dummy) points in a spatial region $B$ has mean zero. For further explanation, see Baddeley et al (2005). The type of residual is chosen by the argument type. Current options are

[object Object],[object Object],[object Object],[object Object]

Use plot.msr to plot the residuals directly, or diagnose.ppm to produce diagnostic plots based on these residuals.

References

Baddeley, A., Turner, R., Moller, J. and Hazelton, M. (2005) Residual analysis for spatial point processes. Journal of the Royal Statistical Society, Series B 67, 617--666.

Baddeley, A., Moller, J. and Pakes, A.G. (2008) Properties of residuals for spatial point processes. Annals of the Institute of Statistical Mathematics 60, 627--649.

Examples

Run this code

data(cells)
    fit <- ppm(cells, ~x, Strauss(r=0.15))

    # Pearson residuals
    rp <- residuals.ppm(fit, type="pe")
    rp

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