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Given a pattern of points X1 and X2, each with quantitative marks, for example growth as diameter. What would be the strategy for bivariate comparison between the X1 and X2 pattern points, using a mark correlation function (markcorr), for example?

I saw in the spatstat book that there are strategies to transform the quantitative marks into qualitative marks, in order to divide them into groups or size classes, and then a bivariate correlation test with the qualitative marks.

However, my objective would be to evaluate how the individuals of a pattern of spots of an sp1 (x1) species with different sizes and diameters, are distributed as a function of size in relation to the pattern of spots of the sp2 species (X2), with also varied diameters. For example, using a bivariate mark correlation function. Is it possible in spatstat? If yes, what is the strategy?

Tieygons
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1 Answers1

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Just to clarify, it seems that you have two point patterns X1 and X2, presumably observed in the same spatial region, and each of these patterns has numerical marks representing something like tree diameter.

For analysis in spatstat it would be best to merge these patterns into a single point pattern with two columns of marks: the first column being the numeric marks (tree diameter) and the second column being a factor that indicates whether the point belonged to pattern X1 or X2. Example:

X1 <- longleaf
X2 <- flipxy(longleaf) # just for example data
Y <- superimpose(X1=X1, X2=X2)

Then you can do, for example,

f <- markcrosscorr(Y)

This will produce a function array (class fasp) of mark correlation functions between each pair of the mark variables (under the assumption that Y is a realisation of a stationary marked point process).

Adrian Baddeley
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  • Exactly, the Mr. be right about the exemple. Thanks, Professor. One more question, what are "OrigMarks" in you exemple? In addition to the two marks (pattern X1 and X2), these marks appeared after `markcrosscorr`. – Tieygons Aug 14 '23 at 23:04
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    @Tieygons "OrigMarks" refer to the original marks of the two point patterns that were superimposed. In `X1` and `X1` the marks are unnamed which is OK since there is only one mark, but in `Y` there are two marks, so they need to have names. `OrigMarks` refer to the original marks (diameter at breast height) while `pattern` refer to which pattern the point belongs to. – Ege Rubak Aug 27 '23 at 12:22