palmdiagnose: Diagnostic based on Palm Intensity

In spatstat.model: Parametric Statistical Modelling and Inference for the 'spatstat' Family

Diagnostic based on Palm Intensity

Description

Given a fitted cluster process or Cox process model, calculate a diagnostic which compares nonparametric and parametric estimates of the Palm intensity.

Usage

palmdiagnose(object, ..., breaks = 30, trim = 30, rmax=Inf)

Arguments

object	Fitted model (object of class "kppm") or a list of fitted models.
...	Optional. Additional arguments which are fitted models of class "kppm".
breaks	Optional argument passed to cut.default determining the breakpoints of distance values for the nonparametric estimate. Either an integer specifying the number of breakpoints, or a numeric vector of distance values to be used as the breakpoints.
trim	Optional. Maximum value of the translation edge correction weight.
rmax	Optional. Maximum interpoint distance r that should be considered. See Details.

Details

This function computes the diagnostic proposed by Tanaka, Ogata and Stoyan (2008, Section 2.3) for assessing goodness-of-fit of a Neyman-Scott cluster process model to a point pattern dataset.

The fitted model object should be an object of class "kppm" representing a Neyman-Scott cluster process model or a Cox process model. In the current implementation, the model must be stationary.

The code computes parametric and non-parametric estimates of the Palm intensity \lambda_0(r), loosely speaking, the intensity of the point process given that there is a point at the origin. The parametric estimate is obtained from the fitted model by substituting the fitted parameter estimates into expressions for the pair correlation and the intensity.

The non-parametric estimate is obtained by considering all pairs of data points, dividing the range of interpoint distances into several equally-spaced bands (determined by the argument breaks), counting the number of pairs of points whose interpoint distances fall in each band, and numerically adjusting for edge effects. Tanaka, Ogata and Stoyan (2008) used the periodic (toroidal) edge correction; our code uses the translation edge correction so that the method can be applied to data in any window.

The result is a function value table (object of class "fv") containing the nonparametric and parametric estimates of the Palm intensity. The result also belongs to the class "palmdiag" which has a method for plot. The default behaviour of plot.palmdiag is to plot the model fit as a curve, and to display the nonparametric estimates as dots; this is the plot style proposed by Tanaka, Ogata and Stoyan (2008). Alternative display styles are also supported by plot.palmdiag.

For computational efficiency, the argument rmax specifies the maximum value of interpoint distance r for which estimates of \lambda_0(r) shall be computed. The default rmax = Inf implies there is no constraint on interpoint distance, and the resulting function object contains estimates of \lambda_0(r) up to the maximum distance that would have been observable in the window containing the original point pattern data.

If there are additional arguments ... which are fitted models of class "kppm", or if object is a list of fitted models of class "kppm", then the parametric estimates for each of the fitted models will be included in the resulting function object. If names are attached to these fitted models, the names will be used in the resulting function object.

Value

Function value table (object of class "fv") containing the nonparametric and parametric estimates of the Palm intensity. Also belongs to the class "palmdiag" which has a plot method.

Author(s)

\adrian

.

References

Tanaka, U., Ogata, Y. and Stoyan, D. (2008) Parameter estimation and model selection for Neyman-Scott Point Processes. Biometrical Journal 50, 1, 43–57.

See Also

plot.palmdiag

Examples

   fitK <- kppm(redwood)
   R <- palmdiagnose(fitK)
   plot(R)

   fitg <- kppm(redwood, statistic="pcf")
   R2 <- palmdiagnose(A=fitK, B=fitg)
   plot(R2)

spatstat.model documentation built on Sept. 30, 2024, 9:26 a.m.