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# Re: st: Interpretation GLM coefficients

 From David Hoaglin To statalist@hsphsun2.harvard.edu Subject Re: st: Interpretation GLM coefficients Date Thu, 19 Jan 2012 07:45:30 -0500

```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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