
Creates an instance of Geyer's triplet interaction point process model which can then be fitted to point pattern data.
Triplets(r)
The interaction radius of the Triplets process
An object of class "interact"
describing the interpoint interaction
structure of the Triplets process with interaction radius
The (stationary) Geyer triplet process (Geyer, 1999)
with interaction radius
Thus the probability density is
The interaction parameter
The nonstationary Triplets process is similar except that
the contribution of each individual point
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 Triplets process pairwise interaction is
yielded by the function Triplets()
. 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 ppm()
, not fixed in
Triplets()
.
Geyer, C.J. (1999) Likelihood Inference for Spatial Point Processes. Chapter 3 in O.E. Barndorff-Nielsen, W.S. Kendall and M.N.M. Van Lieshout (eds) Stochastic Geometry: Likelihood and Computation, Chapman and Hall / CRC, Monographs on Statistics and Applied Probability, number 80. Pages 79--140.
# NOT RUN {
Triplets(r=0.1)
# prints a sensible description of itself
ppm(cells ~1, Triplets(r=0.2))
# fit the stationary Triplets process to `cells'
# ppm(cells ~polynom(x,y,3), Triplets(r=0.2))
# fit a nonstationary Triplets process with log-cubic polynomial trend
# }
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