SRM: A log-link coefficient is a multiplicative effect
In a GLM with log link, a coefficient acts on the log of the conditional mean. Exponentiating gives a multiplicative effect with other predictors fixed. That is not an additive percentage-point change in a probability.
Worked example or practice scenario
If a binary predictor has coefficient .20, its fitted mean ratio is e^.20≈1.2214. With a Poisson count model and exposure offset, the expected count for exposure e is e×exp(linear predictor). Doubling exposure doubles expected count while leaving the fitted rate unchanged.
Try this next
Distinguish the exposure offset from an estimated exposure coefficient. Then explain why a logit-link coefficient instead changes odds, and why multiplying a probability directly by e^.20 can produce an invalid answer.
Reading sources
ActNet editorial guide · October 1, 2026 · Original illustrative examples.