Four link functions are available in the SURVEYLOGISTIC procedure. The logit function is the default. To specify a different link function, use the LINK= option in the MODEL statement. The link functions and the corresponding distributions are as follows:
The logit function
is the inverse of the cumulative logistic distribution function, which is
The probit (or normit) function
is the inverse of the cumulative standard normal distribution function, which is
Traditionally, the probit function includes an additive constant 5, but throughout PROC SURVEYLOGISTIC, the terms probit and normit are used interchangeably, previously defined as .
The complementary loglog function
is the inverse of the cumulative extremevalue function (also called the Gompertz distribution), which is
The generalized logit function extends the binary logit link to a vector of levels by contrasting each level with a fixed level
The variances of the normal, logistic, and extremevalue distributions are not the same. Their respective means and variances are
Distribution 
Mean 
Variance 

Normal 
0 
1 
Logistic 
0 

Extremevalue 


where is the Euler constant. In comparing parameter estimates that use different link functions, you need to take into account the different scalings of the corresponding distributions and, for the complementary loglog function, a possible shift in location. For example, if the fitted probabilities are in the neighborhood of 0.1 to 0.9, then the parameter estimates from using the logit link function should be about larger than the estimates from the probit link function.