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Re: st: Is it valid to use the individual ratios (i.e. Xi/Yi) in the dependent or independent part of a regression model?


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Is it valid to use the individual ratios (i.e. Xi/Yi) in the dependent or independent part of a regression model?
Date   Fri, 25 May 2012 18:51:52 +0100

I imagine each field of statistical science has its own expository
literature on this, e.g.

Kenney, B. C. 1982. Beware of spurious self-correlations!
Water Resources Research 18(4): 1041–1048, doi:10.1029/WR018i004p01041

On Fri, May 25, 2012 at 5:02 PM, Steve Samuels <sjsamuels@gmail.com> wrote:
>
> Rich Goldstein's nice summary contains a reference to Dick Kronmal's article:
>
> Kronmal, R. A. (1993). Spurious correlation and the fallacy of the ratio standard
>  revisited. Journal of the Royal Statistical Society. Series A (Statistics in
>  Society), 379-392.
>
> Dick's thinking (and title) were inspired by:
>
> Tanner, J. M. (1949). Fallacy of per-weight and per-surface area standards,
> and their relation to spurious correlation. Journal of Applied Physiology, 2(1), 1-15.
>
> Happily, Tanner's article is available online:
>
> http://0-jap.physiology.org.library.pcc.edu/content/2/1/1.full.pdf+html
>
> Steve
> sjsamuels@gmail.com
>
>
> Your opening statement is more nearly incorrect than correct. In
> general, X / Y is indeterminate whenever Y is 0; if X and Y are
> normally distributed that is an event with probability 0 (which still
> means possible) but the ratio is otherwise well defined.
>
> If Y is ever 0 in your data then the ratio X / Y is unlikely to make
> scientific sense and so the question of what you can and can't do with
> it statistically doesn't really arise.
>
> I don't think there is a simple answer to whether you should use
> ratios in regression. Often it is scientifically natural; often it is
> pretty dangerous.
>
> For one statement of various pitfalls see list member RIchard
> Goldstein on ratios:
>
> http://biostat.mc.vanderbilt.edu/wiki/pub/Main/BioMod/goldstein.ratios.pdf
>
> Better advice might depend on your giving more details on what you
> want to, mentioning the scientific or medical context as well.
>
> Nick
>
> On Fri, May 25, 2012 at 5:36 AM,  <guhjy@kmu.edu.tw> wrote:
>
>> The ratio of two normally distributed variables (X and Y) has no mean
>> or variance.
>> 1. Why is it valid that the "ratio" command estimates the mean and se of ratios?
>> 2. Is it valid to use the individual ratios (i.e. Xi/Yi) in the
>> dependent or independent part of a regression model?
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