# Bivariate K function for inhomogeneous spatial point processes

I have some inhomogeneous spatial point patterns of individuals in a cactus population. I also have marks, such as "diseased"x "healthy" individuals, and "adult" x "juvenile". I've already computed kinhom and linhom with spatstat for the full poit patterns, but I also want to investigate relations between differently marked individuals. Doing this is quite straightforward in the case of homogeneous point patterns, but what about it in this case of non stationarity? I don't know if stationarity is relevant fo bivariate tests, but my guess is that it is. How to compute for bivariate k function tests for inhomogeneous spatial point processes? Here are the graphs of the K function test for the univariate case (CSR for all individuals irrespective of marks) and the positions with marks, just for illustration.

Thanks a lot. Leila

"The corresponding spatstat functions for inhomogeneous patterns are called Kdot.inhom, Kcross.inhom and Kmulti.inhom."

Prof. Baddeley didn't add anything else to this answer. In trying to make use of his suggestions, I tried to figure it out what exactly each function computes, what's the information each provides. Here's their description at spatstat manual:

kdot.inhom: "For a multitype point pattern, estimate the inhomogeneous version of the dot K function, which counts the expected number of points of any type within a given distance of a point of type i, adjusted for spatially varying intensity."

kcross.inhom:"For a multitype point pattern, estimate the inhomogeneous version of the cross K function, which counts the expected number of points of type j within a given distance of a point of type i, adjusted for spatially varying intensity."

kmulti.inhom: "For a marked point pattern, estimate the inhomogeneous version of the multitype K function which counts the expected number of points of subset J within a given distance from a typical point in subset I, adjusted for spatially varying intensity."

From the descriptions, one can understand that kdot.inhom and kcross.inhom kmulti.inhom compute differences between types (one-to-many and one-to one, respectively), while kmulti.inhom computes differences between subsets (one-to-one). Please let me know if I got it wrong.

If you have a marked point pattern, it seems to me that different types also mean different subsets. This statement discloses the fact that I didn't fully understand the differences... Anyway, I used kmulti.inhom.

• Ok, thank you. I was a little concerned because you guys are always so objective. So I thought it would be better just to provide the sollution. Commented Jul 31, 2015 at 16:23