MAS-I: Exposure belongs in a Poisson count model
For varying observation periods, expected count is exposure times an underlying rate. In a log-link Poisson model, log exposure can enter as an offset with coefficient fixed at one. It is not a free predictor whose effect must be estimated.
Worked example or practice scenario
Two otherwise identical policies have exposures .5 and 1.0 years. If the fitted annual rate is .08, expected counts are .04 and .08. Equal counts would imply different fitted rates, not equal risk.
Try this next
Write the model on both the count and rate scales. Check that a zero exposure is not blindly sent into a logarithm. Then explain how an overdispersion diagnostic can challenge the Poisson variance assumption without changing what exposure means.
Reading sources
ActNet editorial guide · October 1, 2026 · Original illustrative examples.