Gus, I am still not sure what you are doing. What is a bucket? The essence of what you seem to be claiming is that when we sample y to be uniform, then CR gives us the opposite results. You admit, however, that CR works with the usual approach.
In the past I have suggested trimming the tails off normally distributed variables in order to beef up the remaining extremes of the trimmed variable. So I did this just now but trimmed the tails off the y variable. The model is y=x1+x2. x1 and x2 are uniform, y will be triangular. I converted the data to z=scores after generation of the model. I then sorted the data by zy, and deleted all data corresponding to zy above 1.7 and below zy= -1.7. I then calculated C by correlating the absolute values of zy with the absolute differences between zx1 and zx2, and obtained a negative C= -.44. . Thus when the tails of y are trimmed, CR still works. This is consistent with previous simulations I have conducted with many replications. I do not know what you are doing but the method I used took very little time and can be done with excel in a matter of a few minutes. Furthermore, whent the trimming technique is performed on normally distributed x1 and x2, then C/CR works as I suggest. The critical thing is to get enough observations where the causes are paired in both of their extremes. The only effect that trimming the y variable produces (to my knowledge) is a slight restriction in range, thus attenuating the CR effect. Would you mind replicating what I just did and seeing what you find. Bill Chambers PS Gottfried, I think it is a good idea that you collect all the posts on CR. Be sure to include those in which I was banned from SEMNET. OF course, you will not find any comments on SEMNET concerning Marcoulide's fraudulent treatment of the paper they accepted three years ago at the journal Structural Equation Modeling. You have still not expressed one word of disdain for that behavior. Why not throw your opinion of the matter into the 800 posts on CR? That way we can see more clearly which side of honesty you are on. "Gus Gassmann" <[EMAIL PROTECTED]> wrote in message [EMAIL PROTECTED]">news:[EMAIL PROTECTED]... > > > [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. > . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
