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

[guhjy@kmu.edu.tw]

My point is that the mean and se are different between that obtained
by the "ratio" (which is supposedly to be more accurate) and the
"regress" command. Thus, the results obtained by the "regress" command
may be invalid. My question is: how to analyze ratios as the dependent
or independent variables in regression if the mean and se of (Xi/Yi)
is incorrect.
For example:

. webuse census2, clear
(1980 Census data by state)

.
. gen drate1=death/pop

.
. reg drate1

      Source |       SS       df       MS              Number of obs =      50
-------------+------------------------------           F(  0,    49) =    0.00
       Model |           0     0           .           Prob > F      =       .
    Residual |  .000083179    49  1.6975e-06           R-squared     =  0.0000
-------------+------------------------------           Adj R-squared =  0.0000
       Total |  .000083179    49  1.6975e-06           Root MSE      =   .0013

------------------------------------------------------------------------------
      drate1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _cons |    .008436   .0001843    45.78   0.000     .0080657    .0088063
------------------------------------------------------------------------------

.
. ratio (deathrate: death/pop)

Ratio estimation                    Number of obs    =      50

    deathrate: death/pop

--------------------------------------------------------------
             |             Linearized
             |      Ratio   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
   deathrate |   .0087368   .0002052      .0083244    .0091492
--------------------------------------------------------------


Thank you.

Sincerely Yours,
Jinn-Yuh Guh, M.D.
Division of Nephrology
Department of Internal Medicine
Kaohsiung Medical University
100 Zihyou 1st Rd.
Kaohsiung, Taiwan 80756
E-mail:guhjy@kmu.edu.tw
TEL: 886-7-3121101 EXT.7353~12
FAX: 886-7-3228721


2012/5/26 Steve Samuels <sjsamuels@gmail.com>:
>
> 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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