I am working on a study of the spatial distribution of leprosy in an armadillo population. We have point locations for each captured individual and a binary measurement of whether each individual did or did not test positive for leprosy. This sort of marked point pattern is a form of univariate labeled data and I want to do a network (cross) Ripley's K analysis with a conditional randomization test, where the point locations are held constant and the mark (leprosy: yes or no) is permuted among the locations (rather than permuting the locations themselves). I have tried both SANET and GeoDaNet, which do a network version of a cross K analysis, but the randomization scheme seems to be for true bivariate data (not univariate labeled data).
Does anyone know of software that can do a "conditional randomization" test for network (cross) Ripley's K? Our software (PASSaGE 2) can do 1D, 2D, or 3D Ripley's K with this sort of permutation scheme, but not network K.
You can do all those analyses with the spatstats library in R. I have a brief introduction here: http://r-eco-evo.blogspot.com/2008/11/spatial-statistics-part-i.html
Thanks Eric. I did have a look at spatstat before and I did notice that there was some functionality for networks...but I did not see particular functions for network cross K. Is it just a matter of setting the sample space as a network and then using the normal call for K or cross K? Likewise, do you know the function call for the conditional randomization scheme...as I don't want the standard envelope, which, I assume is based on a complete randomization of one the point distributions. The capture distribution is significantly clustered at intermediate distances and so are the locations of individuals with leprosy...and I want to know if the latter is a function of the capture distribution itself or a real pattern. The spatstat package is huge...so I might have overlooked something.
OK....
It looks like function call in R for network K is:
linearK(), linearKcross(), and linearKdot() for comparisons of type i|i, i|j, and i/any, respectively.
However, I am still trying to figure out how to do an i|i comparison with a conditional randomization over all types of points...
Any guesses?
I assume, that if this is possible, then it is a matter of flipping one of the arguments in the envelope.lpp() function....any clue as to which one?
Hello!
Yes, you can do network functions with linearK() for one dimension. And LinearKcross() for two dimensional Ripley. Now, in order to calculate envelopes in a way that the geographic position is fixed, but the labels (sick, not-sick, or male, Female) are randomly shifted among individuals you need to include an option in the envelope command:
envelope(..., simulate=expression(rlabel(X)))
where X is the ppp object (which has labels). In this expression rlabel() randomly assigns one of the labels to the points. That way, the position of the points is kept but the labels are shifted. I think this is what you want.
Hope this help
eric,
Just an update to those of you following this thread.
I finally got this to work in R...but it required some ingenuity.
I originally tried to do this as linearKcross (with an i to i comparison). You can trick spatstat into doing a linearKcross for this scenario by manually setting the i and j arguments to the same mark level (e.g., "Yes" and "Yes"). However, when you try to create the significance envelope it defaults to the i to j comparison.
Instead, what I did was use the split function to create a subset for the mark of interest and then did a linearK for this subpattern. To create the envelope, however, you need to use the entire multitype point pattern, where, for each iteration, you randomize the marks and then split-out the point pattern representing the focal mark.
Here are the function calls I used (with annotation). I am skipping the entire process of creating the lpp (which was a chore).
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LPL
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