On 4/22/2013 9:48 AM, Lorenzo Isella wrote:
Dear All,
I hope this is not too off topic.
I am given a set of scatteplots (nothing too fancy; think about a
normal x-y 2D plot).
I do not deal with two time series (indeed I have no info about time).
If I call A=(A1,A2,...) and B=(B1, B2, ...) the 2 variables (two
vectors of numbers most of the case, but sometimes they can be
categorical variables), I can plot one against the other and I
essentially I need to determine whether
A=f(B, noise) or B=g(A, noise)
where the noise is the effect of other possibly unknown variables,
measurement errors etc.... and f and g are two functions.
Without the noise, if I want to test if A=f(B) [B causes A], then I
need at least to ensure that f(B1)!=f(B2) must imply B1!=B2 (different
effects must have a different cause), whereas it is not ruled out that
f(B1)=f(B2) for B1!=B2 (different causes may lead to the same effect).
However, in presence of the noise, these properties will hold only
approximately so....any idea about how a statistical test, rather than
eyeballing, to tell apart A=f(B, noise) vs B=g(A, noise)?
Any suggestion is welcome.
It strikes me that this is not a particularly productive approach to
causality, particularly in an observational setting. You would need to
design an experiment where you had a known manipulation of an
explanatory variable and studied the change in a response variable, and
then, you came back with the roles reversed. I don't think R or indeed
any statistical package can help you here.
Rob
Lorenzo
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--
Robert W. Baer, Ph.D.
Professor of Physiology
Kirksille College of Osteopathic Medicine
A. T. Still University of Health Sciences
Kirksville, MO 63501 USA
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and provide commented, minimal, self-contained, reproducible code.
