William Chambers wrote:
>
> Guss said:
> >
> >No. You said yourself that you are _selecting_ the x1 and x2 to be
> >uniform.
>
> Yes, we do this so that we will have examples of all combinations of x1 and
> x2,as we would do when using a factorial anova design. But such uniform
> sampling does not make the variables into causes, Adding x1 to x2 causes y,
Here you are using a very different notion of causality than I am
willing to
accept. If you are serious about this notion, then I concede the
argument.
In your sense, of course y is caused by x1 and x2. For me, that is then
simply a "so what?".
> We do not infer that x1 and x2 are the causes because they are uniformly
> sampled. We infer they are the causes because their correlations polarize
> across the ranges of the dependent variable y,
I have to agree with Gottfried Helms and Jerry Dallal and others that
this
is exactly the same thing. Uniform sampling of x1 and x2 _causes_ (in my
sense of the term) y to have a triangular distribution. If y has a
triangular
distribution, then the correlations polarize, by definition.
> >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.
> >
> No it does not, You do not infer that the uniformly sampled variable is the
> cause, You sample the variables you think may be the causes uniformly and
> then see if you get the polarization effect across the ranges of any other
> variables, whether they are uniform or triangular,
In other words, you do have reasons other than purely statistical ones
for
suspecting a causation. You then change the data (by insisting on a
uniform sample) to give you the polarization of the correlations that
you
want. That still looks like circular reasoning to me.
> You are being misled I
> think by Gottfried's speculations about distributions, But Gottfried and I
> have long had a friendly disagreement about this, He sees the presto in the
> distributions, I do not, My point is supported by the fact that you could
> have two variables that are uniformly distributed and a third that is
> triangular and (according to both reality and corresponding
> correlations/regressions) there be no causal relationship between the
> variables.
Exactly. I agree with Gottfried's presto. If you add two uniformly
distributed
variables, the result will be triangular, and the correlations will
polarize.
End of story. What would you say to a model in which
x1 = Annual observations on the number of storks
y = Annual observations on the number of births (of human babies)
If you throw out a few data points so that x1 is nearly uniform, then
you
will see the polarization of correlations. Does that translate into
causation
in your book?
> Furthermore, if you convert the data to ranks after generating
> the y=x1+x2 model based on interval data, then CR still reveals the causal
> pattern.
Of course! Ranks are uniformly distributed. In fact, if you apply
ranking,
then you don't have to use uniform data from the beginning.
> CR does not "know" the data you pass to it are not all uniform,
> It simply looks for the polarization, not for the distribution,
>
> Let's focus this conversation, What do you think about the polarization
> effect, assuming for the moment that it is wise to sample factors uniformly,
> in the way experimenters do in ANOVA designs?
So far I am not impressed, I'm sorry to say.
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