Force Point Process Model to be Valid
Ensures that a fitted point process model satisfies the integrability conditions for existence of the point process.
project.ppm(object, ..., fatal=FALSE, trace=FALSE) ## S3 method for class 'ppm' emend(object, ..., fatal=FALSE, trace=FALSE)
object |
Fitted point process model (object of class |
... |
Ignored. |
fatal |
Logical value indicating whether to generate an error if the model cannot be projected to a valid model. |
trace |
Logical value indicating whether to print a trace of the decision process. |
The functions emend.ppm and project.ppm are identical:
emend.ppm is a method for the generic emend,
while project.ppm is an older name for the same function.
The purpose of the function is to ensure that a fitted model is valid.
First, some of the fitted coefficients of the model
may be NA or infinite values.
This usually occurs when the data are insufficient to estimate
all the parameters. The model is said to be
unidentifiable or confounded.
Second, unlike a regression model, which is well-defined for any finite values
of the fitted regression coefficients, a Gibbs point process model
is only well-defined if the fitted interaction parameters
satisfy some constraints.
A famous example is the Strauss process (see Strauss)
which exists only when the interaction parameter gamma
is less than or equal to 1. For values gamma > 1,
the probability density is not integrable and the process does not
exist (and cannot be simulated).
By default, ppm does not enforce the constraint that
a fitted Strauss process (for example) must satisfy
gamma <= 1.
This is because a fitted parameter value of gamma > 1
could be useful information for data analysis, as it indicates that
the Strauss model is not appropriate, and suggests a clustered model should be
fitted.
The function emend.ppm or project.ppm
modifies the model object
so that the model is valid. It
identifies the terms in the model object
that are associated with illegal parameter values (i.e. parameter
values which are either NA, infinite, or outside their permitted
range). It considers all possible sub-models of object
obtained by deleting one or more
of these terms. It identifies which of these submodels are valid,
and chooses the valid submodel with the largest pseudolikelihood. The result
of emend.ppm or project.ppm is the
true maximum pseudolikelihood fit to the data.
For large datasets or complex models, the algorithm used in
emend.ppm or
project.ppm may be time-consuming, because it takes time to
compute all the sub-models. A faster, approximate
algorithm can be applied by setting
spatstat.options(project.fast=TRUE). This produces a
valid submodel, which may not be the maximum pseudolikelihood submodel.
Use the function valid.ppm to check whether a fitted model
object specifies a well-defined point process.
Use the expression all(is.finite(coef(object))) to determine
whether all parameters are identifiable.
Another point process model (object of class "ppm").
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
fit <- ppm(redwood ~1, Strauss(0.1)) coef(fit) fit2 <- emend(fit) coef(fit2)
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