Link functions are not a SAS topic, you'd need to consult a textbook on logistic regression or generalized linear models.
Basically, if the relationship between the predictors and dependent variable is not assumed to be linear you need to use a different relationship. So you pick the link function that best models your data.
To summarize thebasic ideas, the generalized linear model differs from the general linear model (of which, for example, multiple regressionis a special case) in two major respects: First, the distribution of the dependent or response variable can be (explicitly) non-normal, and does not have to be continuous, i.e., it can bebinomial,multinomial, orordinal multinomial(i.e., contain information on ranks only); second, the dependent variable values are predicted from a linear combination of predictor variables, which are "connected" to the dependent variable via a link function. The general linear model for a single dependent variable can be considered a special case of the generalized linear model: In the general linear model the dependent variable values are expected to follow the normal distribution, and the link function is a simple identity function (i.e., the linear combination of values for the predictor variables is not transformed).
Source: http://www.statsoft.com/Textbook/Generalized-Linear-Models
Exactly how to evaluate and decide which is appropriate is likely a full course so beyond the scope of a post IMO.
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