Force Point Process Model to be Valid
Ensures that a fitted point process model satisfies the integrability conditions for existence of the point process.
- Fitted point process model (object of class
- Logical. Whether to generate an error if the model cannot be projected to a valid model.
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
project.ppm changes the coefficients
in the fitted model
object so that the model is valid.
Because the loglikelihood and log pseudolikelihood are concave,
this simply involves projecting the coefficients onto the boundary
of the parameter space.
Use the function
valid.ppm to check whether a fitted model
object specifies a well-defined point process.
- Another point process model (object of class
fit <- ppm(redwood, ~1, Strauss(0.1)) coef(fit) fit2 <- project.ppm(fit) coef(fit2)