<P> η is expressed as linear combinations (thus, "linear") of unknown parameters β . The coefficients of the linear combination are represented as the matrix of independent variables X . η can thus be expressed as </P> <Dl> <Dd> η = X β . (\ displaystyle \ eta = \ mathbf (X) (\ boldsymbol (\ beta)). \,) </Dd> </Dl> <Dd> η = X β . (\ displaystyle \ eta = \ mathbf (X) (\ boldsymbol (\ beta)). \,) </Dd> <P> The link function provides the relationship between the linear predictor and the mean of the distribution function . There are many commonly used link functions, and their choice is informed by several considerations . There is always a well - defined canonical link function which is derived from the exponential of the response's density function . However, in some cases it makes sense to try to match the domain of the link function to the range of the distribution function's mean, or use a non-canonical link function for algorithmic purposes, for example Bayesian probit regression . </P>

Difference between generalized linear model and linear regression