[EMAIL PROTECTED] wrote:
> Gus,
>
> I am glad that we have both determined that the confidence bands are
> narrower towards the extremes of the predictor when the predictor is y and
> the predicted variable is x1. Conversely, when the predictor is x1 and the
> predicted is y, then the confidence band is wider in the extremes of the
> predictor. I believe this asymmetry in confidence bands allows us to infer
> causation.
>
> You say that you have created subsamples of data in which this does not
> occur but you do not make it clear how you created the subsamples. You say
> that since CR only works with uniformly distributed causes that it is
> invalid. But I have argued for some time that causes should be sampled
> uniformly. Nunnally and others agree with me. The whole set of posts
> concerning the absurdity of normally distributed cell sizes in an anova
> support my thesis. So you are wrong to use normality as a means of
> invalidating CR.
>
> You must be more explicit about how you created the subsamples if I am to
> know what you did.
Fine then. As I said, I created a large set of x1 and x2, each uniformly
distributed
on [-1, 1] and computed y = x1 + x2. I then set out to find a subsample that is
uniformly distributed in x2 and y (on [-0.5,+0.5]). I accomplished this by
defining
10,000 buckets (a 100x100 grid on [-0.5,+0.5] x [-0.5,+0.5]) and into each
bucket
put the first value from the large sample. (e.g. if x1 = 0.375, x2 = -0.217, y =
0.158,
I put this into the bucket labeled (-.22, .16). I can send you the data set if
you want.
Verify two things for me before we go on:
1) y is indeed caused by x1 and x2 (in your theoretical definition of causality)
2) This smaller sample is uniform in x2 and y.
.
.
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