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# Re: st: Interpretation GLM coefficients

 From Fabien Bertho To statalist@hsphsun2.harvard.edu Subject Re: st: Interpretation GLM coefficients Date Thu, 19 Jan 2012 14:15:30 +0100 (CET)

```Hi David,

Yes, it is very helpful. Thank you very much.

I would have one more question concerning the - margins - command. If I use this post-estimation command, can I interpret all coefficients as marginal effects? For instance,

- A one percent change in x2, generate a b2% change in x1
- The movement of x4 from 0 to 1 produces a [exp(b4)-1]% change in x1

And, what is the difference if I include the - atmeans - option or not?

Thank you again for your help.

Fabien

> ----------------------------------------
> From: David Hoaglin <dchoaglin@gmail.com>
> Sent: Thu Jan 19 13:45:30 CET 2012
> To: <statalist@hsphsun2.harvard.edu>
> Subject: Re: st: Interpretation GLM coefficients
>
>
> Hi, Fabien.
>
> Since you are using the log link, the relation between the mean of x1
> and the linear predictor is
>
> mean(x1) = exp(b1 + b2*ln_x2 + b3*x3 + b4*x4), which you can rewrite as
> mean(x1) = exp(b1) * [exp(b2)^ln_x2] * [exp(b3)^x3] * [exp(b4)^x4].
>
> Interpretations often use "incidence rate ratios."
>
> A change of 1 unit in ln_x2 (not a change of 1 percent in x2) would
> change the mean of x1 by a factor of exp(b2).
>
> A change of 1 unit in x3 would change the mean of x1 by a factor of exp(b3).
>
> And changing x4 from 0 to 1 would change the mean of x1 by a factor of exp(b4).
>
> For each variable, the interpretation should include the explanation
> (as applies also in OLS) that the changes are adjusting for the
> contributions of the other variables in the model.  Because the
> predictor variables generally change together in the data, it is an
> oversimplification and often misleading to talk in terms of holding
> the other variables fixed.  (Unfortunately, many textbooks do not
> explain this, but it is an inherent feature of regression-like
> models.)  It may be possible to make predictions that change one
> variable and hold others fixed, as long as you stay within the region
> covered by the data.  Similarly, a change of 1 unit should not take
> you (far) outside that region.
>
> I hope this discussion is helpful.
>
> David Hoaglin
>
> On Thu, Jan 19, 2012 at 4:39 AM, Fabien Bertho
> <fabien.bertho@sciences-po.org> wrote:
> > Hello,
> >
> > I am running glm Poisson regressions and I have some problems in interpreting the coefficients. I am running the following regression:
> >
> > - glm x1 ln_x2 x3 x4, robust cluster(distance) family(poisson) link(log) irls -
> >
> > Where x1 is an integer, x2 and x3 are continuous variables and x4 is a dummy variable.
> >
> > Is the interpretation of glm coefficients different from OLS coefficients? My attempt:
> >
> > => A one percent change in x2, generate a b2 unit change in x1
> > => A one unit change in x3, generate a b3 unit change in x1
> > => The movement of x4 from 0 to 1 produces a b4 unit change in x1
> >
> > Is this correct?
> >
> > Thank you.
> >
> > Best Regards,
> >
> > Fabien BERTHO
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