This session is concerned with summary statistics for interpoint spacing and distances. The lecturer’s R script is available here (right click and save).
rThomas generates simulated realisations of the Thomas model (‘modified Thomas cluster process’).
Read the help file.
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
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
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
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))
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
vcov to estimate the covariance matrix of the parameter estimates.
Compare with the covariance matrix obtained when fitting a homogeneous Poisson model.