Re: st: Odds ratio

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

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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