# 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.

- Keywords
- spatial

##### Usage

`eem(fit)`

##### Arguments

- fit
- The fitted point process model. An object of class
`"ppm"`

.

##### 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'
$$m[i] = 1/lambda-hat(x[i],X)$$
where $lambda-hat(x[i],X)$
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

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

*Documentation reproduced from package spatstat, version 1.6-9, License: GPL version 2 or newer*