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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   guhjy@kmu.edu.tw
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   Sat, 26 May 2012 22:31:15 +0800

It it true that "ratio of means" is less biased than "mean of ratios"
(Comparing Ratio Estimators Based on Systematic Samples:
http://www.isrt.ac.bd/sites/default/files/jsrissues/v40n2/v40n2p1.pdf)?

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 Tirthankar Chakravarty <tirthankar.chakravarty@gmail.com>:
> They estimate two different quantities - you decide which one you want:
>
> *******************************************
> webuse census2, clear
>
> // ratio of means
> ratio (deathrate: death/pop)
> * or, more transparently
> mean death pop
> di _b[death]/_b[pop]
>
> // mean of ratio
> g deathrate = death/pop
> reg deathrate
> * or, more transparently
> mean deathrate
> *******************************************
>
> T
>
> On Sat, May 26, 2012 at 12:19 AM,  <guhjy@kmu.edu.tw> wrote:
>> 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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>>
>> *
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>
>
>
> --
> Tirthankar Chakravarty
> tchakravarty@ucsd.edu
> tirthankar.chakravarty@gmail.com
>
> *
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