The SURVEYLOGISTIC procedure is similar to the LOGISTIC procedure and other regression procedures in the SAS System. See Chapter 58: The LOGISTIC Procedure, for general information about how to perform logistic regression by using SAS. PROC SURVEYLOGISTIC is designed to handle sample survey data, and thus it incorporates the sample design information into the analysis.
The following example illustrates how to use PROC SURVEYLOGISTIC to perform logistic regression for sample survey data.
In the customer satisfaction survey example in the section Getting Started: SURVEYSELECT Procedure in Chapter 99: The SURVEYSELECT Procedure, an Internet service provider conducts a customer satisfaction survey. The survey population consists of the company’s current
subscribers from four states: Alabama (AL), Florida (FL), Georgia (GA), and South Carolina (SC). The company plans to select
a sample of customers from this population, interview the selected customers and ask their opinions on customer service, and
then make inferences about the entire population of subscribers from the sample data. A stratified sample is selected by using
the probability proportional to size (PPS) method. The sample design divides the customers into strata depending on their
types ('Old' or 'New') and their states (AL, FL, GA, SC). There are eight strata in all. Within each stratum, customers are
selected and interviewed by using the PPS with replacement method, where the size variable is Usage
. The stratified PPS sample contains 192 customers. The data are stored in the SAS data set SampleStrata
. Figure 95.1 displays the first 10 observations of this data set.
Figure 95.1: Stratified PPS Sample (First 10 Observations)
Customer Satisfaction Survey 
Stratified PPS Sampling 
(First 10 Observations) 
Obs  State  Type  CustomerID  Rating  Usage  SamplingWeight 

1  AL  New  24394278  Neutral  13.17  26.358 
2  AL  New  64798692  Extremely Unsatisfied  15.53  22.352 
3  AL  New  75375074  Unsatisfied  99.11  3.501 
4  AL  New  262831809  Neutral  5.40  64.228 
5  AL  New  294428658  Extremely Satisfied  1.17  297.488 
6  AL  New  336222949  Unsatisfied  38.69  8.970 
7  AL  New  351929023  Extremely Satisfied  2.72  127.475 
8  AL  New  366142640  Satisfied  2.61  132.958 
9  AL  New  371478614  Neutral  14.36  24.173 
10  AL  New  477172230  Neutral  4.06  85.489 
In the SAS data set SampleStrata
, the variable CustomerID
uniquely identifies each customer. The variable State
contains the state of the customer’s address. The variable Type
equals 'Old' if the customer has subscribed to the service for more than one year; otherwise, the variable Type
equals 'New'. The variable Usage
contains the customer’s average monthly service usage, in hours. The variable Rating
contains the customer’s responses to the survey. The sample design uses an unequal probability sampling method, with the
sampling weights stored in the variable SamplingWeight
.
The following SAS statements fit a cumulative logistic model between the satisfaction levels and the Internet usage by using the stratified PPS sample:
title 'Customer Satisfaction Survey'; proc surveylogistic data=SampleStrata; strata state type/list; model Rating (order=internal) = Usage; weight SamplingWeight; run;
The PROC SURVEYLOGISTIC statement invokes the SURVEYLOGISTIC procedure. The STRATA statement specifies the stratification
variables State
and Type
that are used in the sample design. The LIST option requests a summary of the stratification. In the MODEL statement, Rating
is the response variable and Usage
is the explanatory variable. The ORDER=internal is used for the response variable Rating
to ask the procedure to order the response levels by using the internal numerical value (1–5) instead of the formatted character
value. The WEIGHT statement specifies the variable SamplingWeight
that contains the sampling weights.
The results of this analysis are shown in the following figures.
Figure 95.2: Stratified PPS Sample, Model Information
Customer Satisfaction Survey 
Model Information  

Data Set  WORK.SAMPLESTRATA  
Response Variable  Rating  
Number of Response Levels  5  
Stratum Variables  State  
Type  
Number of Strata  8  
Weight Variable  SamplingWeight  Sampling Weight 
Model  Cumulative Logit  
Optimization Technique  Fisher's Scoring  
Variance Adjustment  Degrees of Freedom (DF) 
PROC SURVEYLOGISTIC first lists the following model fitting information and sample design information in Figure 95.2:
The link function is the logit of the cumulative of the lower response categories.
The Fisher scoring optimization technique is used to obtain the maximum likelihood estimates for the regression coefficients.
The response variable is Rating
, which has five response levels.
The stratification variables are State
and Type
.
There are eight strata in the sample.
The weight variable is SamplingWeight
.
The variance adjustment method used for the regression coefficients is the default degrees of freedom adjustment.
Figure 95.3 lists the number of observations in the data set and the number of observations used in the analysis. Since there is no missing value in this example, observations in the entire data set are used in the analysis. The sums of weights are also reported in this table.
Figure 95.3: Stratified PPS Sample, Number of Observations
Number of Observations Read  192 

Number of Observations Used  192 
Sum of Weights Read  11326.25 
Sum of Weights Used  11326.25 
The “Response Profile” table in Figure 95.4 lists the five response levels, their ordered values, and their total frequencies and total weights for each category. Due
to the ORDER=INTERNAL option for the response variable Rating
, the category “Extremely Unsatisfied” has the Ordered Value 1, the category “Unsatisfied” has the Ordered Value 2, and so on.
Figure 95.4: Stratified PPS Sample, Response Profile
Response Profile  

Ordered Value 
Rating  Total Frequency 
Total Weight 
1  Extremely Unsatisfied  58  2368.8598 
2  Unsatisfied  47  1606.9657 
3  Neutral  44  2594.3564 
4  Satisfied  35  1898.5839 
5  Extremely Satisfied  8  2857.4848 
Probabilities modeled are cumulated over the lower Ordered Values. 
Figure 95.5 displays the output of the stratification summary. There are a total of eight strata, and each stratum is defined by the customer types within each state. The table also shows the number of customers within each stratum.
Figure 95.5: Stratified PPS Sample, Stratification Summary
Stratum Information  

Stratum Index 
State  Type  N Obs 
1  AL  New  24 
2  Old  23  
3  FL  New  25 
4  Old  22  
5  GA  New  25 
6  Old  24  
7  SC  New  24 
8  Old  25 
Figure 95.6 shows the chisquare test for testing the proportional odds assumption. The test is highly significant, which indicates that the cumulative logit model might not adequately fit the data.
Figure 95.6: Stratified PPS Sample, Testing the Proportional Odds Assumption
Score Test for the Proportional Odds Assumption 


ChiSquare  DF  Pr > ChiSq 
617.8597  3  <.0001 
Figure 95.7 shows the iteration algorithm converged to obtain the MLE for this example. The “Model Fit Statistics” table contains the Akaike information criterion (AIC), the Schwarz criterion (SC), and the negative of twice the log likelihood () for the interceptonly model and the fitted model. AIC and SC can be used to compare different models, and the ones with smaller values are preferred.
Figure 95.7: Stratified PPS Sample, Model Fitting Information
Model Convergence Status 

Convergence criterion (GCONV=1E8) satisfied. 
Model Fit Statistics  

Criterion  Intercept Only  Intercept and Covariates 
AIC  35996.656  35312.584 
SC  36009.686  35328.872 
2 Log L  35988.656  35302.584 
The table “Testing Global Null Hypothesis: BETA=0” in Figure 95.8 shows the likelihood ratio test, the efficient score test, and the Wald test for testing the significance of the explanatory
variable (Usage
). All tests are significant.
Figure 95.8: Stratified PPS Sample
Testing Global Null Hypothesis: BETA=0  

Test  ChiSquare  DF  Pr > ChiSq 
Likelihood Ratio  686.0718  1  <.0001 
Score  420.7314  1  <.0001 
Wald  3.9793  1  0.0461 
Figure 95.9 shows the parameter estimates of the logistic regression and their standard errors.
Figure 95.9: Stratified PPS Sample, Parameter Estimates
Analysis of Maximum Likelihood Estimates  

Parameter  DF  Estimate  Standard Error 
Wald ChiSquare 
Pr > ChiSq  
Intercept  Extremely Unsatisfied  1  1.6784  0.3874  18.7741  <.0001 
Intercept  Unsatisfied  1  0.9356  0.3645  6.5900  0.0103 
Intercept  Neutral  1  0.0438  0.4177  0.0110  0.9165 
Intercept  Satisfied  1  0.8440  0.5699  2.1930  0.1386 
Usage  1  0.0350  0.0175  3.9793  0.0461 
Figure 95.10 displays the odds ratio estimate and its confidence limits.
Figure 95.10: Stratified PPS Sample, Odds Ratios
Odds Ratio Estimates  

Effect  Point Estimate  95% Wald Confidence Limits 

Usage  1.036  1.001  1.072 