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GEOSTATS: RE: PhD Question

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  • Vincenzo Matassa
    Dear All I would like to re-phase my question that I posted a few weeks ago. Recently, I was made aware of problems that redundant paths (circular routes) can
    Message 1 of 1 , Oct 4, 1998
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      Dear All
      I would like to re-phase my question that I posted a few weeks
      ago.
      Recently, I was made aware of problems that redundant paths
      (circular routes) can cause in the fit of 'spatial' models of the form;
      Y=pWY+Xt+e. (1)
      Model 1 can be written as ;
      Y=inv(I-pW){Xt+e}; (2)
      But we know that;
      inv(I-pW)=I+pW+(pW)^2+(pW)^3+........ (3)
      From (3) into (2) we get;
      Y=Xt+pWXt + (pW)^2Xt+(pW)^3Xt+.....[1+pW+(pW)^2+...]e

      Automatically powering W can cause 'serious' problems for the estimation
      of the parameters of interst in Model 1. This has been made clear in the
      papers;

      * Blommestein, Hans J . 1985. "elimination of circular Routes in Spatial
      Dynamic regression Equations ", regional Science and Urban Economics, V
      15, p121-130.

      * Anselin, Luc and Smirnov, Oleg 1996 " Efficient Algorithms for
      constructing proper higher order spatial lag operators", Journal
      of Regional Science, V(36), No.1, p67-89.

      My question is 'why' have these 'important' result detailed in these
      papers been ignored in the fitting of spatial auto-regressive model.

      Responses would be appreciated.

      Kind Regards

      Vince



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