The (stationary) Strauss process with interaction radius \(r\) and
parameters \(\beta\) and \(\gamma\)
is the pairwise interaction point process
in which each point contributes a factor \(\beta\) to the
probability density of the point pattern, and each pair of points
closer than \(r\) units apart contributes a factor
\(\gamma\) to the density.
Thus the probability density is
$$
f(x_1,\ldots,x_n) =
\alpha \beta^{n(x)} \gamma^{s(x)}
$$
where \(x_1,\ldots,x_n\) represent the
points of the pattern, \(n(x)\) is the number of points in the
pattern, \(s(x)\) is the number of distinct unordered pairs of
points that are closer than \(r\) units apart,
and \(\alpha\) is the normalising constant.
The interaction parameter \(\gamma\) must be less than
or equal to \(1\)
so that this model describes an ``ordered'' or ``inhibitive'' pattern.
The nonstationary Strauss process is similar except that
the contribution of each individual point \(x_i\)
is a function \(\beta(x_i)\)
of location, rather than a constant beta.
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 the Strauss process pairwise interaction is
yielded by the function Strauss(). See the examples below.
Note the only argument is the interaction radius r.
When r is fixed, the model becomes an exponential family.
The canonical parameters \(\log(\beta)\)
and \(\log(\gamma)\)
are estimated by ppm(), not fixed in
Strauss().