I am running generalized linear regression Gaussian family and log link.

Independent variable is Time (continues variable).

Dependent variables:

  1. years of practice (continues variable). Interpretation something like: each unit increase of years of practice gives increase of what kind of unit? of time?

  2. impact (binary variable, with categories "type one" or "type two"). Interpretation something like: "impact type 2" in comparison to "impact type 2" gives increase of what kind of unit? of time?

How do I interpret results?


1 Answer 1


Let $Y$ be Time (your independent variable), $P$ be years of practice, and $I$ be impact (0 for type one, 1 for type 2).

Then, a glm with Gaussian family and log link fits

$$\log(\mathbb{E}(Y))=\beta_0 + \beta_pP + \beta_II$$

Exponentiating, we get

$$\mathbb{E}(Y) = e^{\beta_0 + \beta_1P + \beta_2I}$$

With a Gaussian family, our model is $$ Y \sim N(e^{\beta_0 + \beta_1P + \beta_2I}, \sigma^2)$$

Note that we can break up the exponential term:

$$e^{\beta_0 + \beta_1P + \beta_2I}=e^{\beta_0}e^{\beta_1P}e^{\beta_2I}$$

The relationship between Y and the predictors is no longer additive as it would be with identity link. Instead, it is multiplicative. For example, a unit increase in $P$ mulitplies the value of the response by $\beta_1$, rather than increasing the response by $\beta_1$. Likewise, a person with impact of type 2 ($I=1$) will have $\beta_2$ times as many years $Y$ as a person with impact of type 1 who has the same number of years in practice $P$.

When performing inference on the coefficients, our estimates for the $\beta$'s do not have an exact Normal distribution, as they do with Gaussian family and identity link. However, there are several methods for testing coefficients that can be run on any glm. @gung's answer gives an excellent overview of the three types.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.