The SURVEYLOGISTIC Procedure
- Overview
- Getting Started
-
Syntax
PROC SURVEYLOGISTIC Statement BY Statement CLASS Statement CLUSTER Statement CONTRAST Statement DOMAIN Statement EFFECT Statement ESTIMATE Statement FREQ Statement LSMEANS Statement LSMESTIMATE Statement MODEL Statement OUTPUT Statement REPWEIGHTS Statement SLICE Statement STORE Statement STRATA Statement TEST Statement UNITS Statement WEIGHT Statement -
Details
Missing Values Model Specification Model Fitting Survey Design Information Logistic Regression Models and Parameters Variance Estimation Domain Analysis Hypothesis Testing and Estimation Linear Predictor, Predicted Probability, and Confidence Limits Output Data Sets Displayed Output ODS Table Names ODS Graphics
-
Examples
- References
Logistic Regression Models
If the response categories of the response variable 
can be restricted to a number of ordinal values, you can fit cumulative probabilities of the response categories with a cumulative logit model, a complementary log-log model, or a probit model. Details of cumulative logit models (or proportional odds models) can be found in McCullagh and Nelder (1989). If the response categories of are nominal responses without natural ordering, you can fit the response probabilities with a generalized logit model. Formulation of the generalized logit models for nominal response variables can be found in Agresti (2002). For each model, the procedure estimates the model parameter 
by using a pseudo-log-likelihood function. The procedure obtains the pseudo-maximum likelihood estimator 
by using iterations described in the section Iterative Algorithms for Model Fitting and estimates its variance described in the section Variance Estimation.
Cumulative Logit Model
A cumulative logit model uses the logit function
 |
as the link function.
Denote the cumulative sum of the expected proportions for the first 
categories of variable by
 |
for 
Then the cumulative logit model can be written as
 |
with the model parameters
 |
 |
 |
|||
 |
 |
 |
|||
 |
|
 |
Complementary Log-Log Model
A complementary log-log model uses the complementary log-log function
 |
as the link function. Denote the cumulative sum of the expected proportions for the first categories of variable by
|
for Then the complementary log-log model can be written as
 |
with the model parameters
|
|
|
|||
|
|
|
|||
|
|
|
Probit Model
A probit model uses the probit (or normit) function, which is the inverse of the cumulative standard normal distribution function,
 |
as the link function, where
 |
Denote the cumulative sum of the expected proportions for the first categories of variable by
|
for Then the probit model can be written as
 |
with the model parameters
|
|
|
|||
|
|
|
|||
|
|
|
Generalized Logit Model
For nominal response, a generalized logit model is to fit the ratio of the expected proportion for each response category over the expected proportion of a reference category with a logit link function.
Without loss of generality, let category 
be the reference category for the response variable . Denote the expected proportion for the th category by 
as in the section Notation. Then the generalized logit model can be written as
 |
for 
with the model parameters
 |
|
 |
|||
|
|
 |