Overdispersion

In Poisson models: observed variance exceeds the mean — the Poisson assumption is violated.

Also known as: overdispersion, dispersion, extra-Poisson variation

Overdispersion appears when count data show greater spread than the Poisson distribution allows: $Var (Y) > E [Y]$ . Causes are usually unobserved heterogeneity (clusters, hidden subgroups) or temporal bursts.

\hat{ϕ} = \frac{Pearson- χ ^{2}}{n - p}

The estimated dispersion parameter $\hat{ϕ}$ should ideally be $\approx 1$ . Values $> 1.5$ indicate clear overdispersion. Consequences and remedies:

Consequence: Poisson standard errors are too small, p-values too optimistic, confidence intervals too tight
Quasi-Poisson — keeps Poisson point estimates, only rescales standard errors by $\hat{ϕ}$
Negative binomial regression — cleaner solution with its own distribution and dispersion parameter $θ$
Model revision — missing important predictors or unmodelled interactions can cause overdispersion

Used in

Regression (Attributive)

In the Algorithm Lab

Sources

Hilbe, J. M. — Negative Binomial Regression, 2nd Edition, Cambridge University Press
McCullagh, P. & Nelder, J. A. — Generalized Linear Models, 2nd Edition, Chapman & Hall

Overdispersion

See also

Used in

In the Algorithm Lab

Sources