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# Re: st: Odds ratio

 From Maarten buis To statalist@hsphsun2.harvard.edu Subject Re: st: Odds ratio Date Fri, 9 Apr 2010 12:47:50 +0000 (GMT)

```--- On Fri, 9/4/10, Richard Williams wrote:
> 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.

I always think of it as a "smart" way of adding a dummy for
each group. For example when you look at persons nested
in schools, this would be a way of adding school dummies.
The whole point of doing random effects models is that we
put some additional constraints on these dummies, e.g.
not correlated with any of the observed variables, etc,
but that is not relevant for this case. The problem with
getting predicted probabilities is that we don't directly
estimate these dummies, so we miss a key set of variables
and coefficients that are necesary for computing the
predicted probabilities.

> 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.

Agreed, using the baseline odds means using the constant, so
you need to scale your explanatory variables so that the
0 makes sense. This is not such a big deal here, because that
should be done anyhow when running a multilevel model.

> 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.

My hypothesis is that that has to do with how we are taught.
We (in continental Europe at least, I don't know much about
the Brits other than that they are sometimes odd) are
trained to think in terms probabilties and the odds only
come in as an afterthought.

-- Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------

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