This section describes how predicted probabilities and confidence limits are calculated by using the pseudoestimates (MLEs) obtained from PROC SURVEYLOGISTIC. For a specific example, see the section Getting Started: SURVEYLOGISTIC Procedure. Predicted probabilities and confidence limits can be output to a data set with the OUTPUT statement.
Let is the th percentile point of a standard normal distribution or a t distribution according to the DF= specification:
For a row vector of explanatory variables , the linear predictor
is estimated by
where and are the MLEs of and . The estimated standard error of is , which can be computed as the square root of the quadratic form , where is the estimated covariance matrix of the parameter estimates. The asymptotic confidence interval for is given by
The predicted value and the confidence limits for Pr are obtained by backtransforming the corresponding measures for the linear predictor.
Link 
Predicted Probability 
Confidence Limits 

LOGIT 


PROBIT 


CLOGLOG 


For a vector of explanatory variables , let denote the probability of obtaining the response value i:
By the delta method,
A 100(1)% confidence level for is given by
where is the estimated expected probability of response i and is obtained by evaluating at .