[R-sig-Geo] 95% CI w/weighted means K value

[Adrian.Baddeley at csiro.au]

This question relates to the pooling of estimates of the K-function from separate point patterns (e.g. replicates of the same experiment
or observations of similar patterns in different survey regions). Alyssa wants to obtain a pooled estimate of the true K-function (assuming all the 
patterns were generated by the same point process) and also a confidence interval for this true K-function.

Simulation envelopes are not relevant here. The data permit direct estimation of the standard error.

The relevant function in the 'spatstat' package is "pool.rat" and it works as follows

   1. For each point pattern dataset, apply Kest() with the argument 'ratio=TRUE', for example K1 <- Kest(X1, ratio=TRUE) where X1 is your first point pattern, and so on.

   2. Pool the K estimates using pool.rat:
               K <- pool(K1, K2, ......, Kn) 
     where K1, K2, ... are the estimates obtained in step 1.
     (Alyssa: this performs weighted averaging as you described)

   3. The object 'K' is the pooled K-function. It's an object of class 'fv' and contains columns like the following:
               pooliso: pooled estimate of K using Ripley's isotropic edge correction
               variso: delta-method estimate of variance of Kest with Ripley's isotropic correction
               hiiso: upper limit of two-sigma confidence interval 
               loiso: lower limit of two-sigma confidence interval
      To see the confidence interval, do something like 
            plot(K, pooliso ~ r, shade=c("hiiso", "loiso"))

For further information including references, see help(pool.rat)

Prof Adrian Baddeley FAA
CSIRO Mathematics, Informatics & Statistics
Leeuwin Centre, 65 Brockway Rd, Floreat WA 6014, Australia
tel +61 8 9333 6177 skype adrian.baddeley
________________________________________

On 30/05/12 08:19, Alyssa W. Pontes wrote:

I have been able to use the envelope function for calculating the
individual K values, but I am combining them using a weighted average and
do not know how to make an envelope for the weighted mean combined K
values, which is what my question relates to.

-Alyssa

On Tue, May 29, 2012 at 3:23 PM, marcelino.delacruz at upm.es<mailto:marcelino.delacruz at upm.es> <
marcelino.delacruz at upm.es<mailto:marcelino.delacruz at upm.es>> wrote:



If you mean Ripley's K (without "correlation") and confidence
envelopes instead of CI, it is very easy with the function pool.envelope
in spatstat.
See the examples in help(pool.envelope)

Cheers,

Marcelino


Con fecha 29/5/2012, "Alyssa W. Pontes" <awpontes at syr.edu><mailto:awpontes at syr.edu> escribió:



I am trying to figure out the Ripley's K correlation between points for 5
replicates.  What I am currently doing is determining the Kcross values


for


each and taking a weighted mean to combine all the replicates into one
value.  Now, what I need to do is determine whether or not this data is
statistically significant.  How do I get a 95% CI for these points with


the


weighted mean?

-Alyssa

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