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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 15:19:58 +0800 |
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/