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I'm using R to run some generalized linear models (GLM) and I want to interpret the estimates.

If I use a GLM assuming Gaussian distribution with identity link, interpretation is easy: if the estimate for factor $x$ is $y$ then an increase of 1 of factor $x$ (if all other factors remain constant) will be estimated to result in a change in the response variable by $y$ units.

Now, if I run a GLM assuming Poisson distribution with log link, in the example above, will the response variable be expected to change by $y$ units, or by $\exp(y)$ units?

note: I'm getting the estimates from summary(model object)


marked as duplicate by gung, Nick Cox, Peter Flom Mar 6 '14 at 17:03

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  • $\begingroup$ Other threads to review include: 1, & 2. $\endgroup$ – gung Mar 6 '14 at 15:58
  • $\begingroup$ Yes, those should be very helpful. It's a good idea to look on the site for the answer to your question - then if something doesn't add up for you, you can post a follow-up question. Also, had you included "Poisson" in your title, i.e. been a bit more spcific, the site would have suggested some relevant links. $\endgroup$ – D L Dahly Mar 6 '14 at 16:11

For a unit change in $x$ you expect the response to change by a factor of $\exp(y)$. So say $\exp(y)=1.5$, then a unit change in $x$ is associated with a $(1.5-1)\times 100\% = 50\%$ increase in the response.


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