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Poisson regression is one of a number of regression models for dependent variables that are counts (non-negative integers). A more general model is negative binomial regression. Both have numerous variants.

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Where does the offset go in Poisson/negative binomial regression?

Recall that an offset is just a predictor variable whose coefficient is fixed at 1. So, using the standard setup for a Poisson regression with a log link, we have: $$\log \mathrm{E}(Y) = \beta' \math …
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