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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   Fri, 09 Apr 2010 08:12:29 -0400

Notre Dame insists that I take valuable time away from Statalist and waste it on teaching classes and the like, so just a few quick comments/questions:

At 02:14 AM 4/9/2010, Maarten buis wrote:
--- On Fri, 9/4/10, Rosie Chen wrote:
> I am doing HLM analysis, so it is impossible to use the Stata
> syntaxt to calculate the predicted probability. So I will
> just do the calculation by myself in excel. Here is what I
> plan to do: I will calculate  log-odds and then convert
> them into predicted probabilities for individuals with
> characteristics that I am interested in so as to demonstrate
> the magnitude of the effect for a specific variable.

Sorry for being blunt but that is a very bad idea. There are
very good reasons why Stata isn't giving you those probabilities
directly: These multilevel models take into account group level
variation, while your approach doesn't.

HLM was a new wrinkle introduced in Rosie's last email. Just to be clear, Maarten, is your criticism specific to HLM models -- i.e. the calculations will be wrong in such cases -- or is it more general than that? I don't do HLM models so I don't know what new complications they introduce.

> For example, in order to explain the gender difference in the
> probability of an outcome, I will compute the difference in
> the predicted probability between females and males

The key issue with odds ratios is that I would like to have the
baseline odds present, to help me interpret the odds ratio (which
in a sense helps to bridge the gap between absolute and relative
effects). The problem is that by default Stata suppresses those.
The trick is to add a variable baseline, which is always one, and
add the -noconstant- option. This trick is discussed in the paper
I refered to before, and I learned it from: Roger Newson (2003),
Stata tip 1: The eform() option of regress. The Stata Journal,
3(4): 445. <http://www.stata-journal.com/article.html?article=st0054>

I agree that the odds ratios become much more useful when you have the baseline odds, although I would still prefer to convert to probabilities. But, you still have to decide on the baseline. Exponentiating the constant gives you the odds for a person who has a score of 0 on every independent variable. If, say, every variable has been centered to have a mean of 0, this may be a good baseline, i.e. you would then be getting the odds for an "average" person. But it is not a good baseline if 0 is not a meaningful value for every variable, e.g. I wouldn't want to use as my baseline somebody who was 0 years old, weighed 0 pounds, and got a score of 0 on a test where the lowest possible score is 400. With what I proposed before, you would try different baselines, e.g. you might compute the probabilities for an "average" male and then compute the probabilities for an otherwise-identical "average" female. You could also do the same for above average and below average males and females.

I am slowely getting used to odds, so the distinction between odds
and probabilities doesn't bother me any more: You can quantify the
likelihood of an event by computing the expected number of success
per 100 trials (100*probability) or by the expected number of
success per failure (the odds). Just don't mix the two up, as
sometimes happens when people try to interpret odds ratios as risk
ratios.

True, but I just had a student who couldn't tell me what the probability of success was if the odds were 3 to 1 in your favor. He said he'd always wondered what that meant. :) Odds aren't that hard to understand but I think probabilities are still easier for most people.


-------------------------------------------
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
WWW:    http://www.nd.edu/~rwilliam

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