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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   Steve Samuels <sjsamuels@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 12:02:26 -0400

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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