William Chambers wrote:
>
> Gus said:
>
> >Here is how I interpret what you've said to date:
>
> >1. If you take two uniformly distributed random variables x1 and x2 and
> >form
> > the sum y = x1 + x2, then y has a distribution that is not uniform.
> >2. If you have two variables x and y and want to determine whether x
> >depends
> > on y or y depends on x, first select the x variable uniformly, then
> >run
> > two regressions, one with each of the two variables as the IV. The y
> > variable is not going to be uniform, of course, but according to you
> > this proves causality.
> >
> >What have I got wrong?
>
> Bill responded:
>
> Well you left out a whole lot of stuff. I have another paper (virus free
> that may help) I will send to you on request that explains things more
> simply, But the essence was expressed in my recent post in which I explained
> the polarization effect, Simply running regressions is not the point, Its
> what kind of regressions (or correlatins), The simplest expression of the
> effect is that the correlations between the two independent variables X1 and
> x2 will be opposite in the extremes versus midranges of y (the dependent
> variable), The correlations between x1 and x2 will not be opposite across
> the ranges of either x variable,
>
> Does this make sense?
No. You said yourself that you are _selecting_ the x1 and x2 to be
uniform.
Of course the Y you generate by adding them will then be triangular. Of
course
the correlations will come out the way you want them to. But does that
prove
causality? Of course not. Look at your model in the opposite direction:
Y is caused by x1 and x2, but I want to prove it isn't, that the
causality
effect is y, x2 => x1. What do I do? I follow your recommendations and
select
the y uniformly and presto: causality goes the other way.
Again I ask: What did I miss?
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