This session covers tools for investigating intensity depending on a covariate. The lecturer’s R script is available here (right click and save).
The bei
dataset gives the locations of trees in a survey area with additional covariate information in a list bei.extra
.
Assign the elevation covariate to a variable elev
by typing
elev <- bei.extra$elev
Plot the trees on top of an image of the elevation covariate.
Cut the study region into 4 areas according to the value of the terrain elevation, and make a texture plot of the result.
Convert the image from above to a tesselation, count the number of points in each region using quadratcount
, and plot the quadrat counts.
Estimate the intensity in each of the four regions.
Assume that the intensity of trees is a function λ(u)=ρ(e(u)) where e(u) is the terrain elevation at location u.
Compute a nonparametric estimate of the function ρ and plot it by
rh <- rhohat(bei, elev)
plot(rh)
Compute the predicted intensity based on this estimate of ρ.
Compute a non-parametric estimate by kernel smoothing and compare with the predicted intensity above.
Bonus info: To plot the two intensity estimates next to each other you collect the estimates as a spatial object list (solist
) and plot the result (the estimates are called pred
and ker
below):
l <- solist(pred, ker)
plot(l, equal.ribbon = TRUE, main = "",
main.panel = c("rhohat prediction", "kernel smoothing"))
Continuing with the dataset bei
conduct both Berman’s Z1 and Z2 tests for dependence on elev
, and plot the results.