GLM: link function and exponential family — connection.

hard

Answer

${\mu}\; = \;E[Y\; \mid \;X]$
$Canonical links: Gaussian \to identity, Bernoulli \to logit, Poisson \to log, Gamma \to inverse.$
$Fit by IRLS (iteratively re-weighted least squares).$
$Advantages over OLS: handles counts, proportions, positive-only outcomes; correct variance structure baked in.$
$Foundation of Poisson regression, logistic regression, gamma regression.$

Check yourself — multiple choice

Only linear
Y ~ exp-family with mean μ, link g(μ) = x'β; canonical: Gaussian-id / Bernoulli-logit / Poisson-log / Gamma-inv; fit via IRLS
Same as OLS
Requires normality

GLM: exp-family + link g(μ)=x'β; canonical links; IRLS fitting.

#regression#glm

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