How to interpret plots of point pattern models

Question

I am struggling with the package spatstat and would really appreciate some help.

I do not know how to interpret the "Fitted trend" and "Estimated SE" plots that one can get with the following code:

library(spatstat)
ppp <- rpoispp(100)
model <- ppm(ppp, ~x+y)
plot(model, pause = F)

I have looked everywhere but everyone seems to assume the reader already knows what they are and what they are for. I am aware the spatstat book Spatial Point Patterns: Methodology and Applications with R might have all the answers I need, but I do not have access to it at the moment.

Any insight will be much appreciated.

edit: I have also looked at the function effectfun which you can plot with:

plot(effectfun(model, "y", se.fit=TRUE))

and which, according to the help page,

Computes the trend or intensity of a fitted point process model as a function of one of its covariates.

but this still doesn't mean much to me, although I understand they must be related in some way.

Answer 1

The fitted trend is simply the estimated intensity of the Poisson process fitted to the data. The intensity is the expected number of points per unit area. So in areas with a high intensity you expect a lot of points and conversely you expect few points in areas of low intensity...

The estimated standard error (SE) is the uncertainty of the intensity estimate.

For more details see Section 9.4 of Spatial Point Patterns: Methodology and Applications with R (Chapter 9 is a free sample chapter available at http://spatstat.github.io/book/ so availability shouldn't be an issue).