Re: st: Odds ratio

[Rosie Chen <jiarongchen2002@yahoo.com>]

Thank you all for the thoughtful responses to my inquiry. Sorry that I did not realize that calculation of probabilities in HGLM and regular one-level logistic model could be different. I guess HLM will complicate this issue further....

Rosie 


----- Original Message ----
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>
Sent: Fri, April 9, 2010 8:12:29 AM
Subject: Re: st: Odds ratio

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.


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Richard Williams, Notre Dame Dept of Sociology
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