# The SURVEYLOGISTIC Procedure

### Linear Predictor, Predicted Probability, and Confidence Limits

Subsections:

This section describes how predicted probabilities and confidence limits are calculated by using the pseudo-estimates (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.

#### Cumulative Response Models

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

where is the percentile point of a standard normal distribution.

The predicted value and the confidence limits for Pr are obtained by back-transforming the corresponding measures for the linear predictor.

Predicted Probability

Confidence Limits

LOGIT

PROBIT

CLOGLOG

#### Generalized Logit Model

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 .