# Why does glm() provide estimates and standard errors on the link scale?

In R, both the parameters estimated by glm() and their standard errors are provided on the link scale, as somebody recently clarified to me here. It makes sense to provide both the parameters and their standard error on the same scale, but then why not display them both in the original scale of the data? I'd imagine that most people are interested in the estimates on the original scale and back-transform them most of the time. While comments to this question address the question on how to back-transform parameter estimates and their standard errors, I am still curious about the reason why such estimates are provided by function summary() on the link scale rather than on the original scale.

• Using standard errors as a summary of uncertainty is generally more reliable on the link scale, where the domain of the parameters is unbounded and where the assumption that the likelihood surface is approximately quadratic ($\leftrightarrow$ sampling distribution of the parameter estimates is approximately Normal) is more likely to be reasonable. For example, suppose you have a log-link model with estimate (on the link scale) 1.0 and standard error 3.0. On the link scale, the confidence interval is approximately $1 \pm 1.96 \times 3$. If you back-transform, exponentiating the parameter and multiplying the standard error by the exponentiated parameter (as in this answer), and then try to construct symmetric CIs, you get $2.718 \pm 1.96 \times 3 \times 2.718$, which includes negative values ... if you do want to back-transform, it makes more sense to back-transform the confidence intervals, i.e. $\exp(1 \pm 1.96 \times 3)$.