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
Rank Correlation of Observed Responses and Predicted Probabilities
The predicted mean score of an observation is the sum of the Ordered Values (shown in the "Response Profile" table) minus one, weighted by the corresponding predicted probabilities for that observation; that is, the predicted means score is 
, where 
is the number of response levels and 
is the predicted probability of the 
th (ordered) response.
A pair of observations with different observed responses is said to be concordant if the observation with the lower ordered response value has a lower predicted mean score than the observation with the higher ordered response value. If the observation with the lower ordered response value has a higher predicted mean score than the observation with the higher ordered response value, then the pair is discordant. If the pair is neither concordant nor discordant, it is a tie. Enumeration of the total numbers of concordant and discordant pairs is carried out by categorizing the predicted mean score into intervals of length 
and accumulating the corresponding frequencies of observations.
Let 
be the sum of observation frequencies in the data. Suppose there are a total of 
pairs with different responses, 
of them are concordant, 
of them are discordant, and 
of them are tied. PROC SURVEYLOGISTIC computes the following four indices of rank correlation for assessing the predictive ability of a model:
 |
|
 |
|||
|
|
 |
|||
|
|
 |
|||
|
|
 |
Note that 
also gives an estimate of the area under the receiver operating characteristic (ROC) curve when the response is binary (Hanley and McNeil 1982).
For binary responses, the predicted mean score is equal to the predicted probability for Ordered Value 2. As such, the preceding definition of concordance is consistent with the definition used in previous releases for the binary response model.