Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 218 / 3 / a

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Time is exposure: doubling the public duration should double the expected count without changing the viewing rate. Modeling the rate is therefore preferable to treating time as an additive linear predictor. In a Poisson regression the exact implementation should be

lo g E (N_{i}) = lo g t_{i} + β_{0} + β_{1} I_{i},

using

lo g t_{i}

as an offset; directly supplying noninteger

N_{i} / t_{i}

without exposure weights is not generally likelihood-equivalent.

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