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.
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
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.
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)
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.
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
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.
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.
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.
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 -------------------------------------------
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.
Customer Satisfaction Survey Score Test for the Proportional Odds Assumption Chi-Square DF Pr > ChiSq 3692.2558 3 <.0001
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.
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
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.
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
Figure 69.9 shows the parameter estimates of the logistic regression and their standard errors.
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
Figure 69.10 displays the odds ratio estimate and its standard error.
Customer Satisfaction Survey Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits Usage 1.038 1.003 1.075