Quasi-Poisson
Section of Standard errors, and models for counts, part of Generalised linear models
Quasi-Poisson
| Type | Section |
| Taught in | Standard errors, and models for counts |
| Part | Generalised linear models |
| Questions using it | 4 |
Unless there is a strong reason to insist on a pure Poisson process, use
\mathrm{Var}(Y_i\mid {\boldsymbol{X}}_i)=\phi\mu_i=\phi\exp({\boldsymbol{X}}_i^\top\boldsymbol{\beta}).
Here \phi>1 is overdispersion and \phi<1 is underdispersion. The case \phi=1 is the Poisson. This is a quasi-Poisson model. The variance function is a legitimate description of spread. Inside the exponential family, a variance exactly proportional to the mean forces the Poisson, so there is no exponential-family distribution with a free \phi in Equation (4) in Standard errors, and models for counts. You cannot simulate a new count from a quasi-Poisson specification alone. We will use it as a description. A stricter view, which reserves the name model for something one can simulate from, would refuse the name. We will come back to that distinction when we treat quasi-likelihood properly. For fitting, glm only needs the mean and the variance, so family = quasipoisson runs.
Used in
- Taught in Standard errors, and models for counts
- Also used in Introduction to generalised linear models · Underdispersion, positive responses, and quasi-likelihood
- Questions that use it (4) — Q47 · Q54 · Question 19 (answer) · C28 (answer)
- All 7 questions on Standard errors, and models for counts
See also
Overdispersion · Underdispersion · Negative binomial distribution · Conway–Maxwell–Poisson distribution · Standard errors in a GLM · Binomial counts in a GLM · Count responses · Reading a log-linear coefficient