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)
- Fitted point process model (object of class
- Logical value indicating whether to generate an error if the model cannot be projected to a valid model.
- Logical value indicating whether to print a trace of the decision process.
First, some of the fitted coefficients of the model
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
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).
ppm does not enforce the constraint that
a fitted Strauss process (for example) must satisfy
$\gamma \le 1$.
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
project.ppm modifies the model
so that the model is valid.
project.ppm identifies the terms in the model
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
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
project.ppm is the true maximum pseudolikelihood fit to the
For large datasets or complex models, the algorithm used in
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
fit <- ppm(redwood, ~1, Strauss(0.1)) coef(fit) fit2 <- project.ppm(fit) coef(fit2)