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


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