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From |
Tirthankar Chakravarty <tirthankar.chakravarty@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 |
Sat, 26 May 2012 01:26:09 -0700 |

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? >> * >> * For searches and help try: >> * http://www.stata.com/help.cgi?search >> * http://www.stata.com/support/statalist/faq >> * http://www.ats.ucla.edu/stat/stata/ >> >> >> * >> * For searches and help try: >> * http://www.stata.com/help.cgi?search >> * http://www.stata.com/support/statalist/faq >> * http://www.ats.ucla.edu/stat/stata/ > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ -- Tirthankar Chakravarty tchakravarty@ucsd.edu tirthankar.chakravarty@gmail.com * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:

**References**:**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

**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>

**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>

*From:*guhjy@kmu.edu.tw

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