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Re: st: Odds ratio


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>, "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Odds ratio
Date   Thu, 08 Apr 2010 16:43:02 -0500

At 01:47 PM 4/8/2010, Rosie Chen wrote:
Hello, dear all,

I have a question regarding a reviewer's comment on my use of odds ratio in interpreting the results of a logistic regression, and would appreciate it very much if you can provide any insight or any references for responding to the comment.

The reviewer commented that all results are expressed in terms of odds ratios which makes it very difficult to assess the magnitude of the effect. Probabilities and changes in probabilities would be much easier to interpret. My impression is that, although it is true that predicted probabilities might be easier to understand, odds ratios have been used extensively in research when we interpret results from logit models. Do you have any suggestions regarding how to respond to this comment, or do you have any statistics textbooks in your mind that recommend odds ratio as a standard approach reporting results from logistic models?

You can probably find a million citations using odds ratios more or less like you are using them, and if that is the norm in your field or in this journal you could argue accordingly. Personally, though, I am sympathetic to the reviewer's comment. It is hard to know what the practical significance of an OR is. Suppose the OR for gender is 100. That might mean, for men, the odds are a million to 1 against, while for women the odds are only 10,000 to 1. That may be a big difference in the odds, but in terms of probabilities it is basically the difference between slim and none. Or, if the OR is 100, it could mean that the odds for men are 1 (50% chance for success) while for women they are 100 (better than 99% chance). That is a huge difference in probabilities.

You may wish to check out Long and Freese's book:

http://www.stata.com/bookstore/regmodcdvs.html

They have all sorts of suggestions on how to make results from logit and ologit models more intuitive and substantively meaningful. For example, one approach is to hold all other variables constant (e.g. at low, average, and high values) and then vary the value of one variable. So, for example, you might find that the "average" women is 30% more likely to succeed than the "average" man. I illustrate some of their approaches on pp. 6-8 of

http://www.nd.edu/~rwilliam/xsoc73994/L12.pdf

Incidentally, this brings up one of my pet peeves about media reports on illnesses or causes of death. You often hear reports that if you do X, you will be 100 times more likely to die from Y. I never know how terrified I should be, since I don't know how likely I am to die from Y if I don't do X. You need some sort of baseline to appreciate what numbers like "100 times more likely" mean in terms of actual probabilities.


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Richard Williams, Notre Dame Dept of Sociology
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