project.ppm: Force Point Process Model to be Valid

Description

Ensures that a fitted point process model satisfies the integrability conditions for existence of the point process.

Usage

project.ppm(object, fatal=FALSE)

Arguments

object

Fitted point process model (object of class "ppm").

fatal

Logical. Whether to generate an error if the model cannot be projected to a valid model.

Value

Another point process model (object of class "ppm").

Details

The model-fitting function ppm fits Gibbs point process models to point pattern data. By default, the fitted model returned by ppm may not actually exist as a point process.

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 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 $\gamma \le 1$. 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 fitted.

The function 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.

Examples

Run this code

fit <- ppm(redwood, ~1, Strauss(0.1))
   coef(fit)
   fit2 <- project.ppm(fit)
   coef(fit2)