Bill said earlier:
>> 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,
>
Gus responded:
>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?".
Bill responded,
In so far as we use numbers to model causes, the causes should also
demonstrate the properties of those numbers, If not we are being deceptive
to use numbers at all, This is point that Michell makes, as referenced in my
most recent paper, We learn more about the phenomenon by what we know about
numbers, This is the whole point of statistics, What do you use numbers
for in causal modeling?
You concede the argument in a manner that suggests I am trying to get away
with something unusual, I most definitely am not. The use of operations to
model causes is implicit through the literature, For example, why do you
think the word "nonadditive" is used to describe interactions in ANOVA?
Bill said:
>> 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,
>Gus responded:
>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.
Bill responded:
First of all, none of you have given an explanation for your beliefs, It
would not matter if every famous statistician in the world made the same
claim, Without an explanation that stands up to the tests of logic, your
claims are not scholarly,
By your definition, if we sample all the variables uniformly, then CR will
not know what to make of the data, In fact, CR will work just as well, I
gave the example of the ranked data below, to which you responded:
Gus said:
>Of course! Ranks are uniformly distributed. In fact, if you apply
>ranking,
>then you don't have to use uniform data from the beginning.
>
Bill responds:
I am ranking them AFTER the causes are first generated using interval or
ratio data, Of course we could use the ranks of the independent variables
in the actual causal generation but their sums would still be triangular, I
do not deny this, only I say it is not enough to warrant causal inference
because other things could cause the triangularity of some variable. I am
saying that if AFTER we get the triangular sums (Y) of the uniform interval,
ratio or ordinal causes, we rank Y, then CR still works..even though the
math is being done on THREE uniform variables, x1, x2 and Y.
You are insisting that the presto is in the distributions, Please explain
why. How does having different distributions allow us to infer causation?
It does not, We could have two uniform variables and a third triangular
variable that is NOT the effect of the two uniform variables,
>
>> >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.
Bill responded:
No. We could simply sample all possible models using uniform distributions
on the current hypothesized causes and the method would still work, The
inference is based completely on the data. Try generating a very large data
set and taking a subsample in which the effect is uniform, See what
happens.
Gus said:
>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.
Bill responded:
Not if you are free to sample every variable under consideration uniformly,
whether you have extra mathematical hunches or not, Thus there is no
circularity,
Furthermore, would you claim that a researcher who samples equally across
the levels of the factors of his anova as loading the experiment? Such
uniform sampling does not cause interactions or main effects, it just allows
for every possibility to be expressed by the data,
>
>> 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.
Gus said::
>
>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.
Bill responded:
This is not even close to the end of the story because when doing research
in the wild you can get triangular variables that are correlated with
uniform variables without any causal relationship. This is because not all
triangular variables will be generated from x1 and x2 (the putative causes).
You are not thinking like an experimenter but are doing what cognitive
scientists call "satisficing." You are jumping to conclusions, Think about
how you would test the assumption that the presto is in the distributions?
You would look for exceptions to the hypothesized rule. If you did so, you
would find the possibility of correlations between uniform variables and
triangular variables without any causal relationship. Would that be
consistent with your belief that the story ends there.
Gus asked:
>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?
Bill responded:
You need to go to a spread sheet and test your understanding of CR/CC
because you are saying things that just are not true, The storks and the
babies represent noncausal correlation, They may both be the function of
something else, such as the number of houses (families) in stork land. But
there are plenty of examples in which we have correlated variables without
causation directly between them. If you read my papers, you will see that CR
and CC do not fall for this illusion, By refusing to consider the
distinction between the distribution of the effect and the polarization
phenomenon, you set your self up for faulty conclusions. At least try them
on the computer before claiming you know what will happen, I have been
working on this stuff since the mid 1980's and have done the simulations,
When you say things like changing the distribution of storks will cause the
artifact of causation, you are not speaking accurately about corresponding
regressions/correlations. Would you like a copy of my most recent paper?
Bill said:
>> 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?
>
Guss said:
>So far I am not impressed, I'm sorry to say.
Bill responded:
I do not think you understand enough yet to be impressed one way or the
other.
Perhaps you would let me know what conditions must be met in order to
impress you. Please be specific.
Bill
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