eem.lppm: Exponential Energy Marks on a Linear Network

In spatstat.linnet: Linear Networks Functionality of the 'spatstat' Family

Exponential Energy Marks on a Linear Network

Description

Given a point process model fitted to a point pattern on a linear network, compute the Stoyan-Grabarnik diagnostic “exponential energy marks” for the data points.

Usage

  ## S3 method for class 'lppm'
eem(fit, ...)

Arguments

fit	The fitted point process model. An object of class "lppm".
...	Ignored.

Details

Stoyan and Grabarnik (1991) proposed a diagnostic tool for point process models fitted to spatial point pattern data. Each point x_i of the data pattern X is given a ‘mark’ or ‘weight’

m_i = \frac 1 {\hat\lambda(x_i,X)}

where \hat\lambda(x_i,X) is the conditional intensity of the fitted model. If the fitted model is correct, then the sum of these marks for all points in a region B has expected value equal to the area of B.

The function eem is generic, with methods for various classes of models. This page documents the method eem.lppm for the class "lppm".

The argument fit must be a fitted point process model on a linear network (object of class "lppm"). Such objects are produced by the fitting algorithm lppm). This fitted model object contains complete information about the original data pattern and the model that was fitted to it.

The value returned by eem is the vector of weights m[i] associated with the points x[i] of the original data pattern. The original data pattern (in corresponding order) can be extracted from fit using response.lppm.

The function diagnose.lppm produces a set of sensible diagnostic plots based on these weights.

Value

A vector containing the values of the exponential energy mark for each point in the pattern.

Author(s)

\spatstatAuthors

.

References

Stoyan, D. and Grabarnik, P. (1991) Second-order characteristics for stochastic structures connected with Gibbs point processes. Mathematische Nachrichten, 151:95–100.

See Also

diagnose.ppm, residuals.lppm, lppm

Examples

    fit <- lppm(spiders ~ x + y)
    ee <- eem(fit)
    sum(ee)/volume(domain(spiders)) # should be about 1 if model is correct

spatstat.linnet documentation built on Jan. 31, 2026, 5:06 p.m.