This session is concerned with summary statistics for spacings and interpoint distances. The lecturer’s R script is available here (right click and save).
library(spatstat)
For the swedishpines
data:
Calculate the estimate of the nearest neighbour distance distribution function G using Gest
.
G <- Gest(swedishpines)
Plot the estimate of G(r) against r
plot(G, cbind(km, rs, han) ~ r, main = "Nearest neighbor distance distribution")
Plot the estimate of G(r) against the theoretical (Poisson) value G_{pois}(r)=1 − exp(−λπr^{2}).
E.g.
plot(G, . ~ theo, main = "Nearest neighbor distribution")
Define Fisher’s variance-stabilising transformation for c.d.f.’s by
Phi <- function(x) asin(sqrt(x))
Plot the G function using the formula Phi(.) ~ Phi(theo)
and interpret it.
Phi <- function(x) asin(sqrt(x))
plot(G, Phi(.) ~ Phi(theo), main = "Nearest neighbor distribution")
The transformation has made the deviations from CSR in the central part of the curve smaller. We need envelopes to say anything about significance.
For the swedishpines
data:
Calculate the estimate of the nearest neighbour distance distribution function F using Fest
.
Fhat <- Fest(swedishpines)
Plot the estimate of F(r) against r
plot(Fhat, main = "Empty Space function")
Plot the estimate of F(r) against the theoretical (Poisson) value F_{pois}(r)=1 − exp(−λπr^{2}).
plot(Fhat, . ~ theo, main = "")
Define Fisher’s variance-stabilising transformation for c.d.f.’s by
Phi <- function(x) asin(sqrt(x))
Plot the F function using the formula Phi(.) ~ Phi(theo)
and interpret it.
Phi <- function(x) asin(sqrt(x))
plot(Fhat, Phi(.) ~ Phi(theo), main = "")
The transformation has changed the picture much. It looks like deviation from CSR, but again, without envelopes it’s hard to draw conclusions.