In a Generalized Linear Model (GLM), why is a link function g(μ)=Xβg(\mu) = X\betag(μ)=Xβ used?
To ensure the variance of the errors is constant.
To map the range of the expected value μ\muμ (which may be restricted) to the entire real line (−∞,∞)(-\infty, \infty)(−∞,∞) where the linear predictor XβX\betaXβ resides.
To transform non-normal data into a normal distribution.
To reduce the number of independent variables in the model.