Getting Started


The SURVEYLOGISTIC procedure is similar to the LOGISTIC procedure and other regression procedures in the SAS System. Please refer to Chapter 42, 'The LOGISTIC Procedure,' for general information about how to perform logistic regression using SAS. PROC SURVEYLOGISTIC is designed to handle sample survey data, and thus it incorporates the sampling 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 'Getting Started' section on page 4422 of Chapter 72, '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 using the probability proportional to size (PPS) method. The sample design divides the customers into strata depending on their types (˜Old' or ˜New') of their states (AL, FL, GA, SC). There are eight strata in all. Within each stratum, customers are selected and interviewed 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 69.1 displays the first 10 observations of this data set.

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  Customer Satisfaction Survey   Stratified PPS Sampling   (First 10 Observations)   Customer                                       Sampling   Obs    State    Type        ID       Rating                    Usage     Weight   1     AL      New       2178037    Unsatisfied               23.53     14.7473   2     AL      New      75375074    Unsatisfied               99.11      3.5012   3     AL      New     116722913    Satisfied                 31.11     11.1546   4     AL      New     133059995    Neutral                   52.70     19.7542   5     AL      New     216784622    Satisfied                  8.86     39.1613   6     AL      New     225046040    Neutral                    8.32     41.6960   7     AL      New     238463776    Satisfied                  4.63     74.9483   8     AL      New     255918199    Unsatisfied               10.05     34.5405   9     AL      New     395767821    Extremely Unsatisfied     33.14     10.4719   10     AL      New     409095328    Satisfied                 10.67     32.5295  
end figure

Figure 69.1: Stratified PPS Sample (First 10 Observations)

In the SAS data set SampleSRS , 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 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 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 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 tables.

PROC SURVEYLOGISTIC first lists the following model fitting information and sample design information in Figure 69.2:

  • 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.

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  Customer Satisfaction Survey   The SURVEYLOGISTIC Procedure   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)  
end figure

Figure 69.2: Stratified PPS Sample, Model Information

Figure 69.3 lists the number of observations in the data set and the number of observations used in the analysis. Since no missing value presents in this example, observations in the entire data set are used in the analysis. The sums of weights are also reported in this table.

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  Customer Satisfaction Survey   Number of Observations Read         192   Number of Observations Used         192   Sum of Weights Read            13262.74   Sum of Weights Used            13262.74  
end figure

Figure 69.3: Stratified PPS Sample, Number of Observations

The 'Response Profile' table in Figure 69.4 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.

start figure
  Customer Satisfaction Survey   Response Profile   Ordered                                   Total            Total   Value     Rating                    Frequency           Weight   1     Extremely Unsatisfied            52        2067.1092   2     Unsatisfied                      47        2148.7127   3     Neutral                          47        3649.4869   4     Satisfied                        38        2533.5379   5     Extremely Satisfied               8        2863.8888   Probabilities modeled are cumulated over the lower Ordered Values.  
end figure

Figure 69.4: Stratified PPS Sample, Response Profile

Figure 69.5 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.

start figure
  Customer Satisfaction Survey   Stratum Information   Stratum   Index     State       Type           N Obs   -------------------------------------------   1       AL          New               22   2                   Old               24   3       FL          New               25   4                   Old               22   5       GA          New               25   6                   Old               25   7       SC          New               24   8                   Old               25   -------------------------------------------  
end figure

Figure 69.5: Stratified PPS Sample, Stratification Summary

Figure 69.6 shows the chi-square test for testing the proportional odds assumption. The test is highly significant, which indicates that the cumulative logit model may not adequately fit the data.

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  Customer Satisfaction Survey   Score Test for the Proportional Odds Assumption   Chi-Square       DF     Pr > ChiSq   3692.2558        3         <.0001  
end figure

Figure 69.6: Stratified PPS Sample, Testing the Proportional Odds Assumption

Figure 69.7 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 (-2 Log L) for the intercept-only model and the fitted model. AIC and SC can be used to compare different models, and the ones with smaller values are preferred.

start figure
  Customer Satisfaction Survey   Model Convergence Status   Convergence criterion (GCONV=1E-8) satisfied.   Model Fit Statistics   Intercept   Intercept            and   Criterion          Only     Covariates   AIC           42099.954      41378.851   SC            42112.984      41395.139     2 Log L      42091.954      41368.851  
end figure

Figure 69.7: Stratified PPS Sample, Model Fitting Information

The table 'Testing Global Null Hypothesis: BETA=0' in Figure 69.8 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.

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  Customer Satisfaction Survey   Testing Global Null Hypothesis: BETA=0   Test                 Chi-Square       DF     Pr > ChiSq   Likelihood Ratio       723.1023        1         <.0001   Score                  465.4939        1         <.0001   Wald                     4.5212        1         0.0335  
end figure

Figure 69.8: Stratified PPS Sample, Testing Global Null Hypothesis

Figure 69.9 shows the parameter estimates of the logistic regression and their standard errors.

start figure
  Customer Satisfaction Survey   Analysis of Maximum Likelihood Estimates   Standard        Wald   Parameter                        DF  Estimate     Error  Chi-Square  Pr > ChiSq   Intercept Extremely Unsatisfied   1   2.0168    0.3988     25.5769      <.0001   Intercept Unsatisfied             1   1.0527    0.3543      8.8292      0.0030   Intercept Neutral                 1    0.1334    0.4189      0.1015      0.7501   Intercept Satisfied               1    1.0751    0.5794      3.4432      0.0635   Usage                             1    0.0377    0.0178      4.5212      0.0335  
end figure

Figure 69.9: Stratified PPS Sample, Parameter Estimates

Figure 69.10 displays the odds ratio estimate and its standard error.

start figure
  Customer Satisfaction Survey   Odds Ratio Estimates   Point          95% Wald   Effect    Estimate      Confidence Limits   Usage        1.038       1.003       1.075  
end figure

Figure 69.10: Stratified PPS Sample, Odds Ratios



SAS.STAT 9.1 Users Guide (Vol. 6)
SAS.STAT 9.1 Users Guide (Vol. 6)
ISBN: N/A
EAN: N/A
Year: 2004
Pages: 127

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