This session is concerned with summary statistics for interpoint spacing and distances. The lecturer’s R script is available here (right click and save).
The command rThomas
generates simulated realisations of the Thomas model (‘modified Thomas cluster process’).
Read the help file.
Type plot(rThomas(10, 0.05, 8))
a few times, and interpret the results.
Experiment with the arguments of rThomas
to obtain point patterns that
Read the help file for kppm
.
Fit the Thomas model to the redwood
data by the method of minimum contrast:
fit <- kppm(redwood ~ 1, clusters="Thomas")
fit
plot(fit)
Read off the parameters of the fitted model, and generate a simulated realisation of the fitted model using rThomas
.
Type plot(simulate(fit))
to generate a simulated realisation of the fitted model automatically.
Try the command
fit2 <- kppm(redwood ~ 1, clusters="Thomas", startpar=c(kappa=10, scale=0.1))
and briefly explore the fitting algorithm’s sensitivity to the initial guesses at the parameter values kappa
and scale
.
Generate and plot several simulated realisations of the fitted model, to assess whether it is plausible.
Extract and plot the fitted pair correlation function by
pcffit <- pcfmodel(fit)
plot(pcffit, xlim = c(0, 0.3))
Type plot(envelope(fit, Lest, nsim=39))
to generate simulation envelopes of the L function from this fitted model. Do they suggest the model is plausible?
Fit a Matern cluster process to the redwood
data.
Use vcov
to estimate the covariance matrix of the parameter estimates.
Compare with the covariance matrix obtained when fitting a homogeneous Poisson model.