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1652[ai-geostats] interpretation of rho in CAR models

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  • Volker Bahn
    Jul 28, 2004
    • 0 Attachment
      Dear list members,

      I created conditional autoregressive regression models for bird incidence
      data of 110 species at a national level in the following way:
      Each model included a unique combination of environmental variables and
      coordinates (the method of variable selection is peripheral to my question
      so I'll omit it here). I created models for 8 neighborhood sizes from 50 to
      400 kms and selected the distance giving the model with the highest log
      likelihood. Thus, the final 110 models have different neighborhood sizes.
      (The neighborhoods also included a spherical distance decay but that's not
      important here.) The equation for CAR models in matrix notation is:
      Y = betaX + rhoC(Y - betaX) + error
      where beta and rho are the coefficients to be determined and C is the
      neighborhood connection matrix.
      In further research I want to relate rho as a measure of the importance of
      neighboring values to other ecological variables. However, I found that in
      my 110 models rho is strongly negatively correlated to the neighborhood
      size. So I considered doing partial correlations of rho against ecological
      variables controlling for the neighborhood size. Do you have any comments,
      insights advice on this issue? Is it acceptable to interpret rho as a
      measure of strength of the spatial effect in the model?

      Thank you

      Volker


      _______________________________

      Volker Bahn

      Dept. of Wildlife Ecology - Rm. 210
      University of Maine
      5755 Nutting Hall
      Orono, Maine
      04469-5755, USA
      Tel. (207) 581 2799
      Fax: (207) 581 2858
      volker.bahn@...
      http://www.wle.umaine.edu/used_text%20files/Volker%20Bahn/home.htm