# 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.

Let is the th percentile point of a standard normal distribution or a t distribution according to the DF= specification:

#### 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

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 .