Hybrid Interaction Point Process Model
Creates an instance of a hybrid point process model which can then be fitted to point pattern data.
- Two or more interactions (objects of class
"interact") or objects which can be converted to interactions. See Details.
A hybrid (Baddeley, Turner, Mateu and Bevan, 2013) is a point process model created by combining two or more point process models, or an interpoint interaction created by combining two or more interpoint interactions. The hybrid of two point processes, with probability densities $f(x)$ and $g(x)$ respectively, is the point process with probability density $$h(x) = c \, f(x) \, g(x)$$ where $c$ is a normalising constant.
Equivalently, the hybrid of two point processes with conditional intensities
$\lambda(u,x)$ and $\kappa(u,x)$
is the point process with conditional intensity
$$\phi(u,x) = \lambda(u,x) \, \kappa(u,x).$$
The hybrid of $m > 3$ point processes is defined in a similar way.
ppm, which fits point process models to
point pattern data, requires an argument
"interact" describing the interpoint interaction
structure of the model to be fitted.
The appropriate description of a hybrid interaction is
yielded by the function
... will be interpreted as interpoint interactions
(objects of class
"interact") and the result will be the hybrid
of these interactions. Each argument must either be an
interpoint interaction (object of class
or a point process model (object of class
"ppm") from which the
interpoint interaction will be extracted.
... may also be given in the form
name=value. This is purely cosmetic: it can be used to attach
simple mnemonic names to the component interactions, and makes the
printed output from
- An object of class
"interact"describing an interpoint interaction structure.
Baddeley, A., Turner, R., Mateu, J. and Bevan, A. (2013)
Hybrids of Gibbs point process models and their implementation.
Journal of Statistical Software 55:11, 1--43.
Hybrid(Strauss(0.1), Geyer(0.2, 3)) Hybrid(Ha=Hardcore(0.05), St=Strauss(0.1), Ge=Geyer(0.2, 3)) fit <- ppm(redwood, ~1, Hybrid(A=Strauss(0.02), B=Geyer(0.1, 2))) fit ctr <- rmhcontrol(nrep=5e4, expand=1) plot(simulate(fit, control=ctr)) # hybrid components can be models (including hybrid models) Hybrid(fit, S=Softcore(0.5)) # plot.fii only works if every component is a pairwise interaction data(swedishpines) fit2 <- ppm(swedishpines, ~1, Hybrid(DG=DiggleGratton(2,10), S=Strauss(5))) plot(fitin(fit2)) plot(fitin(fit2), separate=TRUE, mar.panel=rep(4,4))