Poisson regression: setup and pitfalls.
hardAnswer
- Y ~ Poisson(λ), log λ = x'β.
- Mean = variance = λ (equidispersion).
- Uses: count outcomes (clicks, visits, defects).
- Common pitfall: real data usually over-disperses (Var > Mean).
- Fix: (1) negative binomial regression (extra dispersion parameter), (2) quasi-Poisson (inflates SEs by dispersion factor).
- For zero-heavy counts, use zero-inflated Poisson / negative binomial or hurdle models.
- Always check dispersion after fitting.
Check yourself — multiple choice
- Only for continuous
- Y ~ Poisson(λ), log λ = x'β; assumes Var = Mean — real counts often over-dispersed → use negative binomial / quasi-Poisson / ZIP
- Same as OLS
- Requires normality
Poisson: log λ=x'β; check overdispersion; NB / quasi-Poisson / ZIP fixes.
#regression#glm
Practise Statistics Fundamentals
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