Re: st: Odds ratio

[Richard Williams <Richard.A.Williams.5@ND.edu>]

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.


-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
HOME:   (574)289-5227
EMAIL:  Richard.A.Williams.5@ND.Edu
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