Check Whether Point Process Model is Valid
Determines whether a fitted point process model satisfies the integrability conditions for existence of the point process.
- Fitted point process model (object of class
The model-fitting function
fits Gibbs point process models to point pattern data.
ppm does not check whether the
fitted model actually exists as a point process. This checking
is done by
Unlike a regression model, which is well-defined for any 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
valid.ppm checks whether the fitted model
object specifies a well-defined point process. It returns
TRUE if the model is well-defined.
Another possible reason for invalid models is that the data may not
be adequate for estimation of the model parameters. In this case,
some of the fitted coefficients could be
NA or infinite
values. If this happens
Use the function
project.ppm to force the fitted model
to be valid.
fit1 <- ppm(cells, ~1, Strauss(0.1)) valid.ppm(fit1) fit2 <- ppm(redwood, ~1, Strauss(0.1)) valid.ppm(fit2)