# Pairwise

0th

Percentile

##### Generic Pairwise Interaction model

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

Keywords
models, spatial
##### Usage
Pairwise(pot, name, par, parnames, printfun)
##### Arguments
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.
##### Details

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 $$h(d) = \exp(-\theta \mbox{pot}(d))$$ provided $\mbox{pot}(d)$ 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 $\mbox{pot}(d) = -\infty$. Thus, a potential value of minus infinity is always interpreted as corresponding to $h(d) = 0$, regardless of the sign and magnitude of $\theta$.

##### Value

• An object of class "interact" describing the interpoint interaction structure of a point process.

ppm, pairwise.family, ppm.object

• Pairwise
##### Examples
#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 -6.0
Documentation reproduced from package spatstat, version 1.23-2, License: GPL (>= 2)

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