# Is this the correct way to compute confidence intervals on the original scale for GLM(M)s?

Suppose I have fitted a GLM and want to produce a confidence interval (or a prediction interval) on the original scale of the outcome. What I would do is estimate it on the link scale and then inverse transform the interval.

For example, if I have the output of a Poisson GLM:

> confint(GLM)

2.5 %      97.5 %
(Intercept)  0.7616609  1.90330787
x            0.4118273  1.74089636


Then the intercept would give me:

$$\text{CI}_{95\%} = e^{[0.7616609, \, 1.90330787]} = [2.1, \, 6.7]$$

My question is, is this the right way? Is there a better way to obtain confidence intervals on the original scale? What about prediction intervals?

• Better in what way? Also, I have detailed how one could approximate prediction intervals here by leveraging a normal approximation to the model likelihood Sep 11, 2021 at 18:29
• That is great, I will definitely have a look at your post Sep 11, 2021 at 18:37
• I just wondered if there were a more efficient method, perhaps providing narrower intervals? Sep 11, 2021 at 18:53