# eem

##### Exponential Energy Marks

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, 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`

.

##### 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 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.

##### Value

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

##### 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

##### Examples

```
# 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")
# }
```

*Documentation reproduced from package spatstat, version 1.63-0, License: GPL (>= 2)*