Smoothed partial residuals of a covariate in a point process model in spatstat

Question

I am using spatstat to build point process models using the ppm function but I have problems in validation, when I use the residual plot parres to understand the effect of a covariate.

The model is composed of 1022 locations of bird occurrences (called ois.ppm ), the habitat availability (a raster called FB0lin which has been normalized and log-transformed), the sampling effort (a raster called Nbdate , normalized too) and the accessibility of places (a raster called pAccess , normalized too) across the study area. The objective is to evaluate the fit of a Gibbs point process model with a Geyer process parameter, the habitat availability, the sampling effort and the accessibility. The eps function was also used to create a set of dummy points chosen along a grid with a 100 x 100 m resolution.

The model used is: mod.ois.echlin = ppm(ois.ppp, ~ FB0lin + Nbdate + pAccess, interaction = Geyer(r=401,sat=9), eps=100)

Geyer parameter were identified using: rs=expand.grid(r=seq(1,1001, by=50), sat=1:40) term.interlin=profilepl(rs, Geyer, ois.ppp,~FB0lin+Nbdate+pAccess)

Then I use the parres function: res.FB0.echlin=parres(mod.ois.echlin, covariate="FB0lin") plot(res.FB0.echlin,main="FB0 LinCost", legend=FALSE)

The problem is that the fitted values seems not to be optimal (see figure below). The fit curve should have lower values within interval confidence but is outside of this interval, which probably affect the quality of the point process model.

My questions are then:

• Have you ever seen such a result and is it normal?
• is it possible to correct it?

Figure: Smoothed partial residuals - FB0lin

Any advice would be much appreciated.

Answer 1

The diagnostic is working correctly. It indicates that, as a function of the predictor variable FB0lin , the fitted model (represented by the dashed straight line) overestimates the true intensity of the model (represented by the thick black curve with grey confidence bands) by a constant amount. The linear relationship (linear dependence of the log intensity on the covariate) seems to be adequate, in the sense that you don't need to replace this linear relationship by a more complicated relationship (which is the main question for which the partial residuals are used). The diagnostic says that the model is adequate except that it is underestimating the log intensity by a constant amount, which means that it is underestimating the intensity by a constant factor. (This could be due to the way in which the other predictors Nbdate and pAccess are involved in the model, or it could be due to the choice of interpoint interaction. To investigate that, you need to try other tools as discussed in Chapter 11 of the spatstat book .)