On Nov 20, 8:48 am, djh <halitsk...@att.net> wrote: > I. U-Relativization/Dependence > > Thanks a lot for considering the ?u-relativization? proposal. > > Please confirm that what you mean by this: > > ?The usual first step is to take it to be linear, which would add u^2 > to the regression of c on u, > u & u*e to the regression of c on e, and u*e & u^2 to the multiple > regression of c on e & u.? > > are the three regressions: > > c on (u,u^2) instead of c on u > > c on (e, u, u*e) instead of c on e > > c on (e, u, u*e, u^2) instead of c on (e,u)
> > Or did you mean ?add? arithmetically, e.g. c on u+u^2 instead of c on > u, etc.?
> > (Fortunately, I?m sufficiently automated now to do these new > regressions with only the obvious changes to one program in which I > call the GSL regression functions; so the re-reruns will not be > onerous.)
But interpreting the coefficients is no longer straightforward, and you might have to write new code. This is a BIG topic, that needs its own post, if not its own thread, and I don't want to get into it here.
> > II. Question about the centroids > > I was a little taken aback by your reaction to the ?centroids? > suggestion: > > > ?So all you're suggesting is to look at some linear transformations > > of the centroids of the points at each L. That can never tell you > > anything about the within-L relations or if/how they change with L.? > > until I realized that: > > i) in my own mind, I was proposing the centroid analysis as part of an > entirely different approach to the problem; > > ii) I hadn?t yet communicated this new approach to you yet (Whoops!) > > So, to keep things simple, suppose we agree for the sake of discussion > that: > > a) there IS a discoverable function F such that L = F(c,e,u);
I hope you don't expect exact equality. L,c,u are all based on counts and have no measurement error, right? From the statistical point of view, the model would be e = G(L,c,u) + error; you would regress e on L,c,u.
> > b) it?s worth trying to discover F because knowing how to predict L > from (c,e,u) would be an important first step toward predicting > structural alignability (this is the part I won?t bother to explain > now ? again, to keep things simple.)
Does it make sense to talk about "predicting" L? Is it possible to get c,e,u experimentally without knowing L?
> > Then, given the proposed transformation of the (L,c,e,u) 4-space into > a 3-space containing a 2-space projection of (c,e,u) and an L-axis > orthogonal to this space: > > c) isn?t it at least possible that as L increases, the path traversed > by the centroid might provide some clues as to the nature of F? (E.g. > might even be something like some kind of smooth space curve?)
That would allow you to rule out potential F's, that did not map the centroids into the corresponding L's.