Reference no: EM133423636

In this problem set, we will again analyze the spatial patterns of healthy and diseased myrtle trees, which are infected with Myrtle Wilt. Reuse the data files from problem set 6, which contain point patterns of the locations of healthy and diseased trees.

To fit point process models, we first need to convert the shapefiles to ppp format. The 'ppm' function doesn't work on marked point patterns, so we also need to strip away the marks. The following code does those steps:

library(raster)
library(spatstat)
library(maptools)

d <- shapefile("Diseased.shp") # Remember to set your working directory to
h <- shapefile("Healthy.shp") # the location where these files are stored

d.unmarked <- unmark(as.ppp(d))
h.unmarked <- unmark(as.ppp(h))

Questions

1. Fit a point process model of a stationary Poisson process to each point pattern. What is the intensity of each point pattern?

2. Consider the hypothesis that the density of trees of each type changes along an East-West gradient. For each point pattern, fit a point process model of a non-stationary Poisson process with an intensity function λ = e a+bx. For each point pattern, use AIC to determine if the model is better than the model you fit in Q1.

3. Consider the hypothesis that the tree density is a non-linear function of the ?? coordinate. For each point pattern, fit a point process model of a non-stationary Poisson process with an intensity function λ = e a+bx+cx 2. For each point pattern, use AIC to determine if the model better than the model you fit in Q2.