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

`eem(fit, check=TRUE)`

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`

.

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

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 argument `fit`

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 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 `data.ppm`

.

The function `diagnose.ppm`

produces a set of sensible diagnostic plots based on these weights.

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

# NOT RUN { 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") # }