Kest (spatstat) and "r" values

Hello,

I am employing the Ripley's K function to evaluate my data and have some
concerns regarding the maximum distance reported.

My data was collected in 7 different sites. At each site we recorded the
location x-y of the events. The 7 sites were had *"similar conditions"
*but their
extent vary, and in addition, not all sites presented the same number of
events (number of events per site vary from 92 to up to 400 ).

Each site was evaluated independently, meaning that Site-1 had their on set
of events and own window of observation (W). I used the *ripras* function
to define *W, *(for all sites, W is an irregular shaped window).

I have run two first order exploratory  tools
(quadrat.test, clarkevans.test). The overall results is that my
observations are not random and show aggregation tendencies for all sites.


I applied the function* Kest* to all my seven sites to explore the second
order properties, I did not provide a *r* value (as recommended in the help
section) and here is the "curious" outcome. Indifferently of the area of W
or the number  of events per site, the maximum r-values reported for all
sites is very similar (between 5000 m to  6140 m). I am trying to
understand the reason behind these results. Is this an overall
characteristic of my pattern OR is a result of the algorithm that spatstat
employs to define r (e.g. it has a maximum threshold)

Here my code:

K2<-Kest(site2,correction="best"); where site2 is mydata
max(K2$r) = 5,260 m

Here the maximum distance values (in meters) for the other sites

max(K1$r) = 6,140
max(K3$r) = 5,148
max(K4$r) = 5,016
max(K5$r) = 5,194
max(K6$r) = 5,055
max(K3$r) = 5,317

PS: I used the extent of the observation window for site 2 to create a
random set of x-y locations (n=182, same than the observed number of events
in this site). I run the test and the maximum distance was the same (5,260
m)

I cannot find information how r is defined in the function Kest

If any one any comment I will appreciate

Thank you!

Silvia Cordero-Sancho

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Maybe the information related to r you are looking for is in the Warning
section:

"Warnings

The estimator of K(r) is approximately unbiased for each fixed r. Bias
increases with r and depends on the window geometry. For a rectangular
window it is prudent to restrict the r values to a maximum of 1/4 of the
smaller side length of the rectangle".

Maybe I'm wrong but I think that  Kest computest K(r) by default for r
up to 1/4 of the shorter side of the *enclosing rectangle* of your window.