Generalized linear models allow for an arbitrary link function, g, that relates the mean of the response variable(s) to the predictors: E ( Y ) = g − 1 ( X B ) {\displaystyle E(Y)=g^{-1}(XB)} . The link function is often related to the distribution of the response, and in particular it typically has the effect of transforming between the ( − ∞ , ∞ ) {\displaystyle (-\infty ,\infty )} range of the linear predictor and the range of the response variable.