R: Exponential Energy Marks

eem {spatstat.core} | R Documentation

## Exponential Energy Marks

### Description

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

### Usage

      eem(fit, ...)

      ## S3 method for class 'ppm'
    eem(fit, check=TRUE, ...)

      ## S3 method for class 'slrm'
    eem(fit, check=TRUE, ...)

### Arguments

`fit` | The fitted point process model. An object of class `"ppm"`.
`check` | Logical value indicating whether to check the internal format of `fit`. 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 computed, set `check=TRUE`.
`...` | 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] = 1/λ(x[i],X)

where λ(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 argument `fit` must be a fitted point process model (object of class `"ppm"` or `"slrm"`). Such objects are produced by the fitting algorithms `ppm`) and `slrm`. 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`.

The function `diagnose.ppm` 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)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner r.turner@auckland.ac.nz

### 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`, `ppm.object`, `data.ppm`, `residuals.ppm`, `ppm`

### Examples

        data(cells)
        fit <- ppm(cells ~x, Strauss(r=0.15))
        ee <- eem(fit)
        sum(ee)/area(Window(cells)) # should be about 1 if model is correct
        Y <- setmarks(cells, ee)
        plot(Y, main="Cells data\n Exponential energy marks")

[Package spatstat.core version 2.4-4 Index]