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# Re: st: Modelling two binary outcomes that are not mutually exclusive

 From SamL To statalist@hsphsun2.harvard.edu Subject Re: st: Modelling two binary outcomes that are not mutually exclusive Date Sat, 27 Nov 2004 08:05:32 -0800 (PST)

```I don't understand why you wouldn't use a bivariate probit model.  It is
my understanding that this model is designed for 2 binary outcomes.  The
error terms in the two equations are allowed to be correlated (the
correlation is estimated).  Many people use this with one equation being a
"selection" equation, but that is not required.  If I understand your
issue correctly, this would be an appropriate model--not multinomial
logit.

Hope this helps.
Sam

On Sat, 27 Nov 2004, Ronán Conroy wrote:

> I have two binary outcomes, measured in a patient population (anxiety
> and depression). For various reasons, I suspect that a number of patient
> characteristics predict depression but not anxiety.
>
> If the two diagnoses were mutually exclusive, all would be well. I could
> use multinomial logistic regression and compare the coefficients.
> However, there is about a 20% overlap. Is this a Known Problem? I could
> model the overlap category as a third outcome, and show that the
> coefficients were similar to those for depression alone and different to
> those for anxiety alone, but this is slicing the sample a little thin -
> there are just 8 people with both disorders. (This approach actually
> works, sort of, given the small numbers, so I'm on the right track from
> the theory point of view.)
>
> Any suggestions out there?
>
> --
>
> Ronan M Conroy (rconroy@rcsi.ie)
> Senior Lecturer in Biostatistics
> Royal College of Surgeons
> Dublin 2, Ireland
> +353 1 402 2431 (fax 2764)
> --------------------
> Just say no to drug reps
> http://www.nofreelunch.org/
>
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