Receiving different measured values from crossK and lohboot

Question

I have a marked ppp dataset looking at crimes and their relation to locations.

I am performing an inhomogeneous cross-K using the Kcross.inhom, and am using lohboot to bootstrap confidence intervals around the inhomogenous cross-K. However, I am getting different measured values of the iso for the two when we would anticipate identical values.

The crime dataset is 26k rows, unsure of how to subset to create a reproducible example.

#creating the ppp
crime.coords = as.data.frame(st_coordinates(crime))  #coordinates of crimes
center.coords = as.data.frame(st_coordinates(center)) #coordinates of locations 
temp = rbind(data.frame(x=crime.coords$X,y=crime.coords$Y,type='crime'),
             data.frame(x=center.coords$X,y=center.coords$Y,type='center')) #df for maked ppp
temp = ppp(temp[,1],temp[,2], window=owin(border.coords), marks=relevel(as.factor(temp$type), 'crime')) #creating marked ppp


#creating an intensity model of the crimes
temp = rescale(temp, 10000) #rescaling for polynomial model coefficients
crime.ppp = unmark(split(temp)$crime)
model.crime = ppm(crime.ppp ~ polynom(x, y, 2), Poisson())

ck = Kcross.inhom(temp, i = 'crime', j = 'center', lambdaI = model.crime) #cross K w/ intensity function
ckenv = lohboot(temp, fun='Kcross.inhom', i = 'crime', j='center', lambdaI = model.crime) #bootstrapped CIs for cross K w/ intensity function

Here are the values plotted, showing different curves:

A few things I've noted are that the r are different for both functions, and setting the lohboot r does not in fact make them identical. Unsure of where to go from here, exhausted all my resources in finding a solution. Thank you in advance.

Answer 1

These curves are not guaranteed to be equal. lohboot subdivides the data, randomly resamples the subdivisions, computes the contributions from these randomly selected subdivisions, and averages them. If you repeat the experiment you should get a slightly different answer from lohboot each time. See the help file for lohboot.

It would desirable that the two curves are close. Unfortunately the default behaviour of lohboot does not often achieve that. For consistency, the default behaviour follows the original implementation which was not very good. Try setting block = TRUE for better performance. Also try the other options basicboot and Vcorrection.