Generic Pairwise Interaction model
Creates an instance of a pairwise interaction point process model which can then be fitted to point pattern data.
Pairwise(pot, name, par, parnames, printfun)
pot |
An R language function giving the user-supplied pairwise interaction potential. |
name |
Character string. |
par |
List of numerical values for irregular parameters |
parnames |
Vector of names of irregular parameters |
printfun |
Do not specify this argument: for internal use only. |
This code constructs a member of the
pairwise interaction family pairwise.family
with arbitrary pairwise interaction potential given by
the user.
Each pair of points in the point pattern contributes a factor h(d) to the probability density, where d is the distance between the two points. The factor term h(d) is
h(d) = exp(-theta * pot(d))
provided pot(d) is finite, where theta is the coefficient vector in the model.
The function pot must take as its first argument
a matrix of interpoint distances, and evaluate the
potential for each of these distances. The result must be
either a matrix with the same dimensions as its input,
or an array with its first two dimensions the same as its input
(the latter case corresponds to a vector-valued potential).
If irregular parameters are present, then the second argument
to pot should be a vector of the same type as par
giving those parameter values.
The values returned by pot may be finite numeric values,
or -Inf indicating a hard core (that is, the corresponding
interpoint distance is forbidden). We define
h(d) = 0 if pot(d) = -Inf.
Thus, a potential value of minus infinity is always interpreted
as corresponding to h(d) = 0, regardless of the sign
and magnitude of theta.
An object of class "interact"
describing the interpoint interaction
structure of a point process.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
#This is the same as StraussHard(r=0.7,h=0.05)
strpot <- function(d,par) {
r <- par$r
h <- par$h
value <- (d <= r)
value[d < h] <- -Inf
value
}
mySH <- Pairwise(strpot, "StraussHard process", list(r=0.7,h=0.05),
c("interaction distance r", "hard core distance h"))
data(cells)
ppm(cells, ~ 1, mySH, correction="isotropic")
# Fiksel (1984) double exponential interaction
# see Stoyan, Kendall, Mecke 1987 p 161
fikspot <- function(d, par) {
r <- par$r
h <- par$h
zeta <- par$zeta
value <- exp(-zeta * d)
value[d < h] <- -Inf
value[d > r] <- 0
value
}
Fiksel <- Pairwise(fikspot, "Fiksel double exponential process",
list(r=3.5, h=1, zeta=1),
c("interaction distance r",
"hard core distance h",
"exponential coefficient zeta"))
data(spruces)
fit <- ppm(unmark(spruces), ~1, Fiksel, rbord=3.5)
fit
plot(fitin(fit), xlim=c(0,4))
coef(fit)
# corresponding values obtained by Fiksel (1984) were -1.9 and -6.0Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.