Your client wants factors driving natural gas usage per account, but the raw data holds total therms and account counts. Do you divide first, weight the model, or bolt on an offset? Each choice changes the coefficients, and the exam rewards knowing which lever fits the question.
Why exposure breaks a naive count model. Suppose you model claim counts across policies. A policy in force twelve months should produce more claims than one in force two months, purely from time exposed. If you regress raw counts on rating factors, the model confuses "more exposure" with "riskier." You want to model the rate, claims per unit of exposure, while still fitting on the count scale that Poisson likelihood expects.
The offset fixes this. An offset is a term you add to the linear predictor with its coefficient pinned to 1. You do not estimate it. For a Poisson model with a log link, you want the expected count proportional to exposure.
Common mistakes
- Supplying exposure instead of log-exposure. With a log link the offset lives on the link scale. Passing raw exposure instead of log(exposure) breaks proportionality. The offset should be log of exposure, not exposure.
- Forgetting the offset at prediction time. predict needs the offset variable in newdata. Leave it out and R predicts for a single unit of exposure, understating the count by the exposure multiple.
- Copying the offset-versus-weight answer into the weight-versus-predictor part. October 2024 graders flagged this directly. Part (b) requires GLM-specific weight-versus-predictor content, not recycled OLS offset material.
Bottom line
- An offset is a predictor whose coefficient is fixed at 1, added on the link scale, never estimated.
- Use a log offset (log of exposure) in a Poisson count model to model a rate per unit of exposure.
- A weight scales how much each observation contributes to the likelihood; it changes precision, not the systematic mean.
- Offsets shift the fitted mean; weights change the variance and the influence of each row.
Exam shortcut
Match the verb to the tool: "per unit of exposure," "per policy-year," or "rate" signals an offset, and with a log link the offset is always log(exposure). "Each row summarizes many records" or "averages of different-sized groups" signals a weight, weighted by the group size.
The full lesson (about 2,463 words, 16 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- 4b
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