# Hybrid

##### Hybrid Interaction Point Process Model

Creates an instance of a hybrid point process model which can then be fitted to point pattern data.

##### Usage

`Hybrid(...)`

##### Arguments

- …
Two or more interactions (objects of class

`"interact"`

) or objects which can be converted to interactions. See Details.

##### 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.

The function `ppm`

, which fits point process models to
point pattern data, requires an argument
of class `"interact"`

describing the interpoint interaction
structure of the model to be fitted.
The appropriate description of a hybrid interaction is
yielded by the function `Hybrid()`

.

The arguments `…`

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 `"interact"`

),
or a point process model (object of class `"ppm"`

) from which the
interpoint interaction will be extracted.

The arguments `…`

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 `print.ppm`

neater.

##### Value

An object of class `"interact"`

describing an interpoint interaction structure.

##### References

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.
http://www.jstatsoft.org/v55/i11/

##### See Also

##### Examples

```
# NOT RUN {
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))
# }
```

*Documentation reproduced from package spatstat, version 1.64-1, License: GPL (>= 2)*