# Re: st: Binomial regression

 From "Tim Wade" To statalist@hsphsun2.harvard.edu Subject Re: st: Binomial regression Date Fri, 3 Aug 2007 11:20:48 -0400

```Thanks Constantine for sharing your results.

There are certainly cases where the risk difference is a more
appropriate  or desirable measure. In these cases,  the identity link
does have the significant advantage of being linear on the probability
scale instead of the log odds scale. And while we can convert log-odds
to probability, it is often convenient, especially when we have a
multivariate model to be able to interpret the regression coefficients
as the expected change in the probability (i.e, the risk difference)
holding other factors constant. Since probability is not linear in the
logistic model,  similar inferences about probability or risk
differences cannot be made with the logistic model. If one wants to
make a statement about risk differences from multivariate logistic
model, it needs to be with regard to holding the other covariates at
some specific constant value, such as zero or at their mean values.

Tim

On 8/2/07, Marcello Pagano <pagano@hsph.harvard.edu> wrote:
> Sorry to disagree with your first sentence, Constantine.
> Logistic regression stipulates a linear relationship of covariates with
> the log of the odds of an event (not odds ratios).
>  From this it is straightforward to recover the probability (or risk, if
> you prefer that label) of the event.
> Don't understand your aversion to logistic regression to achieve what
> you want to achieve.
> If you don't like the shape of the logistic, then any other cdf will
> provide you with a transformation to obey the constraints inherent in
> modeling a probability.  The uniform distribution that you wish to use
> has to be curtailed, as others have pointed out.
> m.p.
>
>
> > No argument about logistic regression. But that gives you odds ratios.
> > What if you want risk differences instead?
> >
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```