PrintFinally, we will introduce second-order interaction effects using one spatial process that can produce evenly spaced patterns (rSSI) and one that produces clustered patterns (rThomas).
Note that there are other available processes in the spatstat package in R (e.g., evenly-spaced patterns using rMaternI(), rMaternII() and clustered patterns using rMatClust() as well as rCauchy(), rVarGamma(), rNeymanScott(), rGaussPoisson()). You can feel free to experiment with those if you are interested to do so. You can find out about the parameters they require with a help command:
> help("rMaternI")
rSSI is the Simple Sequential Inhibition process.
> pp <- rSSI(a, N)
where a specifies the inhibition distance and N specifies the number of events.
Events are randomly located in the study area (which by default is a 1-by-1 square, with x and y coordinates each in the range 0 to 1), but, if an event is closer to an already existing event than the inhibition distance, it is discarded. This process continues until the required number of events (N) have been placed. As the inhibition distance is reduced, the resulting pattern is more like something that might be generated by IRP/CSR, although events are still not completely independent of one another.
rThomas is a clustering process.
> pp <- rThomas(a, b, N)
a specifies the intensity of a homogeneous Poisson process (i.e., IRP/CSR), which produces cluster centers.
b specifies the size of clusters as the standard deviation of a normally distributed distance from each cluster center. This means that events are most likely to occur close to cluster centers, with around 95% falling within twice this distance of centers, and very few fall more than three times this distance from cluster centers.
N specifies the expected number of events in each cluster.
Experiment with at least these two models (rSSI and rThomas) to see how changing their parameter values changes the spatial pattern in the plots. In your experimentation, I suggest varying one parameter while keeping the other parameter(s) constant until you understand the parameter's behavior. Use the R commands we've already introduced in the earlier parts of this lesson in your explorations of the homogeneous and inhomogeneous Poisson processes to create graphics to illustrate your write-up.
Deliverable
Now, using examples of patterns that you generated by the rSSI() and rThomas() models to illustrate uniformity and clustered patterns, comment on the following topics/questions in your Project 3A write-up:
- Explain the basics of how each of the rSSI() and rThomas() models work.
- Do all the created patterns appear random?
- How do the patterns differ from the random patterns you generated in the first section, if at all?
- Discuss whether it is possible to visually identify that 2nd order effects are influencing the locations of events in these patterns.