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RE: [APBR_analysis] Dan, I admit that I haven't been following these discussions very closely

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  • Michael Tamada
    ... From: jsm_44092 [mailto:tpr42345@aol.com] Sent: Monday, March 29, 2004 9:38 AM because I don t have time, but when I see your discussions of the
    Message 1 of 2 , Mar 29, 2004
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      -----Original Message-----
      From: jsm_44092 [mailto:tpr42345@...]
      Sent: Monday, March 29, 2004 9:38 AM

      because I don't have time, but when I see your discussions of the
      regressions that you have run I am reminded of the fact that
      regression coefficients really don't have any meaning for
      ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
      nonorthogonal data, which of course is the type of data with which
      ^^^^^^^^^^^^^^^^^^
      you are working. I believe there is a better approach. I see
      that the UNC-G library has a copy of my regression book ("Modern
      Regression Methods") and I suggest that you look at pages 472-475 of
      my book. Some programming work would certainly be required,
      especially for the number of predictors that you are using, but I
      believe that the project would be doable. We can discuss this if you
      want to go in that direction.


      *** Our library does not have a copy of _Modern Regression Methods_
      so I'm going to have to ask for clarification on this.

      If by non-orthogonal data, you mean that some of the explanatory
      variables are correlated with each other, then practically every
      regression that's ever been run has non-orthogonal data.

      And I don't understand how the coefficients don't have any meaning.
      They have meaning in terms of marginal effects, holding all other
      variables constant. If you mean that it's dangerous to extrapolate
      from them, that's correct -- e.g. to apply them as average effects
      would require strong assumptions about linearity. And to try to
      assign percent of variation explained to individual explanatory
      variables is also futile with non-orthogonal variables. But the
      coefficients still have meaning.

      Or maybe your comment is refering to a key assumption of the standard
      least squares regression model: that the explanatory variables are
      non-stochastic. When they do have randomness in them, things can
      get bad, and when that randomness is correlated with the residual
      term (or error term), then things get worse -- we have endogeneity,
      aka simultaneity bias. But there are regression techniques for
      dealing with these, if they truly are a problem (quite often they
      are not, even when the explanatory variables do come from some
      stochastic process).

      I haven't had time to look in detail at DanR's regression results,
      but regardless of what's in his results, I don't understand the
      highlighted comment. Taken at face value, what you're doing is
      trashing about a century of statistical work.


      --MKT
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