What is quasi-likelihood?

hard

Answer

$\operatorname{Var}(Y)\; = \;{\varphi}\; \cdot \;V({\mu})$
$Quasi-scores solve exact same equations as MLE for the mean, but SEs use estimated dispersion φ.$
$Quasi-Poisson: V(μ) = μ, φ estimated \to same β as Poisson but corrected SEs.$
$Cheap fix when the distribution isn't quite right — used extensively in industry counting problems.$

Check yourself — multiple choice

Same as MLE
Specify only mean-variance relationship (Var = φ·V(μ)); same β as MLE, SEs corrected by dispersion φ; standard fix for overdispersed counts
Not real
Requires normality

Quasi-likelihood: mean-var relation only; corrects SEs via dispersion φ.

#regression#glm

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