rspatstat

Envelope for pooled mark correlation functions

I wish to create an envelope for mark correlation functions (in my example, mark variogram, but this should apply to any of them) pooling field replicates from what's assumed to be the same point process. While having read the documentation available for each of those steps in isolation, I couldn't find much about the application of pooling and envelopes to mark correlation functions. In the following I'll illustrate my attempt by recreating in an example, at the best of my abilities, with longleaf and a jittered copy of it (despite being meaningless, it should suffice).

longleaf2 <- rjitter(longleaf, radius=10, retry = T)

list <- solist(longleaf, longleaf2)

vario <- lapply(list, function(x) envelope(x, markvario, nsim = 39, 
                                           simulate=expression(rlabel(x)), savefuns=T))

pool <- pool(as.anylist(vario))
plot(pool)

While the output seems reasonable, I have no assurance about this procedure being sound. Additionally, while the envelope shading is plotted with this example, it's not with my data, and forcing it with plot.envelope returns an error. Alternatively, the answer to this question seems to suggest pooling first, then making envelopes, but there's no fv method for envelope as far as I know.

Solution

  • There are several questions here.

    Firstly about the validity of pooling:

    While the output seems reasonable, I have no assurance about this procedure being sound.

    Pooling several envelope objects involves extracting all the simulated functions from all the envelopes, and constructing a new envelope object based on these simulated functions. If that is valid in your context, then the procedure is valid.

    Validity depends on how the simulated functions were generated. In your case, if there are several different point pattern datasets, and you generate an envelope for each data point pattern using rlabel to randomise the marks, then I think it is not valid to pool these envelopes, because the summary functions in one envelope are not exchangeable with the summary functions from another envelope.

    Next about the computational procedure:

    Additionally, while the envelope shading is plotted with this example, it's not with my data, and forcing it with plot.envelope returns an error.

    So... the example given in the question is working as desired,... but with your data it doesn't work? Please provide a minimal working example where the procedure does not work.

    In your example, vario is a list, each element of which is an envelope object. Then the pool command is dispatched to pool.anylist which invokes pool.envelope. Then the result is an envelope object.

    In your actual data (which you didn't show us) the first thing would be to check that you have a list of envelope objects, e.g.

    all(sapply(vario, inherits, what="envelope"))

    If this is FALSE then the result of pool will not be an envelope object.