
The short answer is that you are estimating different intensities. 
With "at points" you are estimating intensities at each of your 
points. WIth "at pixels", you are estimating intensities at the 
central point of each pixel (by the way, you can define the grid of 
pixels that you want; by default the grid is 100 x 100).

So, with "at pixels" you are not estimating the intensity "at 
points", obviously... But you are telling Kcross.inhom to use that 
intensity to "correct" your Kcross. Kcross.inhom will take for each 
point the intensity in the nearest pixel. See the diffeferent values:

 > lambdaM
  [1] 49.41339 45.80276 44.62354 31.24124 41.84972 55.37315 50.39604 55.25678
  [9] 57.22046 55.43888 50.79079 54.12046 56.82362 63.17133 62.82282 60.14551
[17] 50.65605 32.40867 65.76905 61.29220 62.98508 63.01079 64.13257 73.87368
[25] 64.88419 74.30606 78.91268 78.16282 77.85479 75.40066 78.44332 67.55195
[33] 63.26124 54.28607 48.79299 50.29495 46.28902 34.42021 34.14865 42.64884
[41] 65.99603 62.84123 68.54072 78.27751 78.46927 69.71036 67.20497 60.28367
[49] 62.04037 30.56103 35.62552 11.66438
attr(,"sigma")
[1] 0.15

 >  lambdaM.px[ma]
  [1] 62.66350 57.45939 53.85413 39.67402 48.85228 64.62754 58.72627 65.71949
  [9] 65.64248 62.97430 64.84507 61.56765 63.63711 70.73357 70.19060 67.59623
[17] 59.31942 43.87235 72.89798 68.64034 70.09329 70.68119 71.42198 81.31944
[25] 73.08050 85.09178 92.79973 87.00091 85.48162 83.20746 85.91217 74.53052
[33] 70.29730 61.05902 56.10340 58.00092 54.63235 45.37311 41.89826 51.58081
[41] 73.35583 70.13251 76.61496 92.63824 88.57151 89.81377 83.88502 71.40912
[49] 75.78562 43.49678 44.75833 27.05462

These last are the intensity values that Kcross.inhom will use for 
"ma" when you use "at pixels". As these values are larger than the 
values "at points", the estimate of Kcross will be smaller.


A let the long answer for Adrian or Rolf, ;-)

Cheers,

Marcelino


At 19:12 20/02/2011, Mudrak, Erika [EEOBS] wrote:
>I would like to use the function Kcross.inhom, but I'm confused 
>about ways to supply the lambda intensity vaules (arguments lambdaI 
>and lambdaJ)
>
>The help file says you can supply image files for these arguments, 
>or if you omit values for these arguments, then it will be estimated 
>using a 'leave-one-out' kernel smoother through density.ppp.
>
>My confusion is why you get different values if you use density.ppp 
>to generate an image file with either at="points" (creating a 
>numeric vector of intensity values at the points) or at="pixels" 
>(creating an image showing intensities at every location in a fine 
>grid of the window).
>
>The examples in the help file show this done with density.ppp using 
>at=points, yet the default value in this function is at="pixels".
>
>An extension to the examples given in the help file (see below- 
>method 3) show that K1 and K2 are equivalent (estimate values ABOVE 
>the theoretical Poisson line), but K3 (using the image produced from 
>density.ppp) is highly different (with estimate values BELOW the 
>theoretical Poisson line).
>
>Can someone explain to me the difference?
>
>Thank you!
>
>Erika
>
>
>     # Lansing Woods data
>
>     data(lansing)
>
>     lansing <- lansing[seq(1,lansing$n, by=10)]
>
>     ma <- split(lansing)$maple
>
>     wh <- split(lansing)$whiteoak
>
>     # method (1): estimate intensities by nonparametric smoothing
>     lambdaM = density.ppp(ma, sigma=0.15, at="points")
>     lambdaW = density.ppp(wh, sigma=0.15, at="points")
>     K1 = Kcross.inhom(lansing, "whiteoak", "maple", lambdaW, lambdaM)
>     plot(K1)
>
>     # method (2): leave-one-out
>     K2 = Kcross.inhom(lansing, "whiteoak", "maple", sigma=0.15)
>     plot(K2)
>
>      # method (3): MY ADDITION
>     lambdaM.px = density.ppp(ma, sigma=0.15)    #default at="pixels"
>     lambdaW.px = density.ppp(wh, sigma=0.15)    #default at="pixels"
>     K3 = Kcross.inhom(lansing, "whiteoak", "maple", lambdaW.px, lambdaM.px)
>     plot(K3)
>
>Erika Mudrak
>Postdoctoral Researcher
>Ecology, Evolution, and Organismal Biology
>Bessey Hall 253
>Iowa State University
>mudrak@iastate.edu
>
>
>         [[alternative HTML version deleted]]
>
>_______________________________________________
>R-sig-Geo mailing list
>R-sig-Geo@r-project.org
>https://stat.ethz.ch/mailman/listinfo/r-sig-geo

____________________________________

Marcelino de la Cruz Rot
Depto. Biologia Vegetal
EUIT Agricola
Universidad Politecnica de Madrid

tel: 34 + 913365435
____________________________________  
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