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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?

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

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