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What is a Generalized Linear Model and when is it the right tool?

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Answer

  • A GLM has three ingredients: (1) a linear predictor η=w⊤x\eta = \mathbf{w}^{\top}\mathbf{x}; (2) a link function gg relating η\eta to E[y∣x]\mathbb{E}[y \mid x], so g(μ)=ηg(\mu) = \eta; (3) a distribution from the exponential family for yy (Gaussian → linear regression, Bernoulli → logistic, Poisson → Poisson regression, Gamma → Gamma regression).
  • Use a GLM when your target has a known non-Gaussian distribution but the mean-predictor relationship is approximately linear on the right scale.
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  • GLM only means Generalized Linear Model = regularized regression
  • It combines a linear predictor, a link function, and an exponential-family distribution
  • GLM is always logistic regression
  • GLM requires normally distributed y

Linear predictor + link + exponential-family distribution ⇒ Gaussian, logistic, Poisson, etc.

#linear-regression#linear-models#theory

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