Negative binomial regression — why use it?

hard

Answer

$\operatorname{Var}\; = \;{\mu}\; + \;{\mu}^{2} / {\theta}$
$Handles over-dispersion (Var > Mean) which is the norm for real counts (customer visits, defect counts, rare events).$
$Fit by MLE.$
$When θ \to \infty \to reduces to Poisson.$
$\operatorname{exp}({\beta})$
$Modern default for count regression in industry.$

Check yourself — multiple choice

Same as Poisson
NB: $\operatorname{Var}\; = \;{\mu}\; + \;{\mu}^{2} / {\theta}$ → models overdispersion; reduces to Poisson as θ → ∞; industry default for counts
Only for binary
Random

Negative binomial: extra dispersion → handles overdispersed counts.

#regression#glm

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