Topic summary
Link function
Extracted from the Wikipedia article Generalized linear model.
Link function
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.