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