Diggle-Gates-Stibbard Point Process Model
Creates an instance of the Diggle-Gates-Stibbard point process model which can then be fitted to point pattern data.
DiggleGatesStibbard(rho)
rho |
Interaction range |
Diggle, Gates and Stibbard (1987) proposed a pairwise interaction point process in which each pair of points separated by a distance d contributes a factor e(d) to the probability density, where
e(d) = sin^2((π * d)/(2 * ρ))
for d < ρ, and e(d) is equal to 1 for d ≥ ρ.
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 Diggle-Gates-Stibbard
pairwise interaction is
yielded by the function DiggleGatesStibbard().
See the examples below.
An object of class "interact"
describing the interpoint interaction
structure of the Diggle-Gates-Stibbard
process with interaction range rho.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk
Baddeley, A. and Turner, R. (2000) Practical maximum pseudolikelihood for spatial point patterns. Australian and New Zealand Journal of Statistics 42, 283–322.
Ripley, B.D. (1981) Spatial statistics. John Wiley and Sons.
Diggle, P.J., Gates, D.J., and Stibbard, A. (1987) A nonparametric estimator for pairwise-interaction point processes. Biometrika 74, 763 – 770. Scandinavian Journal of Statistics 21, 359–373.
DiggleGatesStibbard(0.02) # prints a sensible description of itself ppm(cells ~1, DiggleGatesStibbard(0.05)) # fit the stationary D-G-S process to `cells' # ppm(cells ~ polynom(x,y,3), DiggleGatesStibbard(0.05)) # fit a nonstationary D-G-S process # with log-cubic polynomial trend
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