| eem {spatstat} | R Documentation |
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.
|
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 {hatλ(x_i,X)}
where hatλ(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.
A vector containing the values of the exponential energy mark for each point in the pattern.
Adrian Baddeley adrian@maths.uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner rolf@math.unb.ca http://www.math.unb.ca/~rolf
Stoyan, D. and Grabarnik, P. (1991) Second-order characteristics for stochastic structures connected with Gibbs point processes. Mathematische Nachrichten, 151:95–100.
diagnose.ppm,
ppm.object,
data.ppm,
residuals.ppm,
ppm
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\n Exponential energy marks")