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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? * * 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/

**Follow-Ups**:**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

**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>

**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

*From:*Nick Cox <njcoxstata@gmail.com>

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