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.
Solved – Why does glm() provide estimates and standard errors on the link scale
generalized linear modelrstandard error
Best Answer
Hard to know for sure, but there are a few reasons the link scale is useful.
Probably the proximal reason is that because of the issues listed above, most people who do a lot of statistical modeling have gotten used to interpreting parameters on the link scale; most epidemiologists and biostatisticians have to spend time learning about odds ratios and log-odds ratios, and there are lots of papers written about their interpretation. For better or worse, R was written by people who are comfortable interpreting parameters on the link scale. Many downstream packages such as broom have options that will exponentiate parameters and CIs for you (putting them on the data (count) scale for the log link; the odds-ratio scale for logit links; and the hazard-ratio scale for cloglog links).