Getting Started
This section demonstrates how you can use PROC SURVEYREG to perform a regression analysis for sample survey data. For a complete description of the usage of PROC SURVEYREG, see the section 'Syntax' on page 4373. The 'Examples' section on page 4395 provides more detailed examples that illustrate the applications of PROC SURVEYREG.
Simple Random Sampling
Suppose that, in a junior high school, there are a total of 4,000 students in grades 7, 8, and 9. You want to know how household income and the number of children in a household affect students' average weekly spending for ice cream.
In order to answer this question, you draw a sample using simple random sampling from the student population in the junior high school. You randomly select 40 students and ask them their average weekly expenditure for ice cream, their household income, and the number of children in their household. The answers from the 40 students are saved as a SAS data set:
data IceCream; input Grade Spending Income Kids @@; datalines; 7 7 39 2 7 7 38 1 8 12 47 1 9 10 47 4 7 1 34 4 7 10 43 2 7 3 44 4 8 20 60 3 8 19 57 4 7 2 35 2 7 2 36 1 9 15 51 1 8 16 53 1 7 6 37 4 7 6 41 2 7 6 39 2 9 15 50 4 8 17 57 3 8 14 46 2 9 8 41 2 9 8 41 1 9 7 47 3 7 3 39 3 7 12 50 2 7 4 43 4 9 14 46 3 8 18 58 4 9 9 44 3 7 2 37 1 7 1 37 2 7 4 44 2 7 11 42 2 9 8 41 2 8 10 42 2 8 13 46 1 7 2 40 3 9 6 45 1 9 11 45 4 7 2 36 1 7 9 46 1 ;
In the data set IceCream , the variable Grade indicates a student's grade. The variable Spending contains the dollar amount of each student's average weekly spending for ice cream. The variable Income specifies the household income, in thousands of dollars. The variable Kids indicates how many children are in a student's family.
The following PROC SURVEYREG statements request a regression analysis:
title1 'Ice Cream Spending Analysis'; title2 'Simple Random Sample Design'; proc surveyreg data=IceCream total=4000; class Kids; model Spending = Income Kids / solution anova; run;
The PROC SURVEYREG statement invokes the procedure. The TOTAL=4000 option specifies the total in the population from which the sample is drawn. The CLASS statement requests that the procedure use the variable Kids as a classification variable in the analysis. The MODEL statement describes the linear model that you want to fit, with Spending as the dependent variable and Income and Kids as the independent variables . The SOLUTION option in the MODEL statement requests that the procedure output the regression coefficient estimates. The ANOVA option requests that the procedure output the ANOVA table.
Figure 71.1 displays the summary of the data, the summary of the fit, and the levels of the classification variable Kids . The 'Fit Statistics' table displays the denominator degrees of freedom, which are used in F tests and t tests in the regression analysis.
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Ice Cream Spending Analysis Simple Random Sample Design The SURVEYREG Procedure Regression Analysis for Dependent Variable Spending Data Summary Number of Observations 40 Mean of Spending 8.75000 Sum of Spending 350.00000 Fit Statistics R-square 0.8132 Root MSE 2.4506 Denominator DF 39 Class Level Information Class Variable Levels Values Kids 4 1 2 3 4
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Figure 71.1: Summary of Data
Figure 71.2 displays the ANOVA table for the regression and the tests for model effects. The effect Income is significant in the linear regression model, while the effect Kids is not significant at the 5% level.
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Ice Cream Spending Analysis Simple Random Sample Design The SURVEYREG Procedure Regression Analysis for Dependent Variable Spending Tests of Model Effects Effect Num DF F Value Pr > F Model 4 119.15 <.0001 Intercept 1 153.32 <.0001 Income 1 324.45 <.0001 Kids 3 0.92 0.4385 NOTE: The denominator degrees of freedom for the F tests is 39.
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Figure 71.2: Testing Effects in the Regression
The regression coefficient estimates and their standard errors and associated t tests are displayed in Figure 71.3.
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Ice Cream Spending Analysis Simple Random Sample Design The SURVEYREG Procedure Regression Analysis for Dependent Variable Spending Estimated Regression Coefficients Standard Parameter Estimate Error t Value Pr > t Intercept 26.084677 2.46720403 10.57 <.0001 Income 0.775330 0.04304415 18.01 <.0001 Kids 1 0.897655 1.12352876 0.80 0.4292 Kids 2 1.494032 1.24705263 1.20 0.2381 Kids 3 0.513181 1.33454891 0.38 0.7027 Kids 4 0.000000 0.00000000 . . NOTE: The denominator degrees of freedom for the t tests is 39. Matrix X'X is singular and a generalized inverse was used to solve the normal equations. Estimates are not unique.
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Figure 71.3: Regression Coefficients
Stratified Sampling
Suppose that the previous student sample is actually drawn using a stratified sample design. The strata are grades in the junior high school: 7, 8, and 9. Within strata, simple random samples are selected. Table 71.1 provides the number of students in each grade.
| Grade | Number of Students |
|---|---|
| 7 | 1,824 |
| 8 | 1,025 |
| 9 | 1,151 |
| Total | 4,000 |
In order to analyze this sample using PROC SURVEYREG, you need to input the stratification information by creating a SAS data set with the information in Table 71.1. The following SAS statements create such a data set called StudentTotals :
data StudentTotals; input Grade _TOTAL_; datalines; 7 1824 8 1025 9 1151 ;
The variable Grade is the stratification variable, and the variable _TOTAL_ contains the total numbers of students in each stratum in the survey population. PROC SURVEYREG requires you to use the keyword _TOTAL_ as the name of the variable that contains the population total information.
In a stratified sample design, when the sampling rates in the strata are unequal , you need to use sampling weights to reflect this information. For this example, the appropriate sampling weights are the reciprocals of the probabilities of selection. You can use the following data step to create the sampling weights:
data IceCream; set IceCream; if Grade=7 then Prob=20/1824; if Grade=8 then Prob=9/1025; if Grade=9 then Prob=11/1151; Weight=1/Prob;
If you use PROC SURVEYSELECT to select your sample, PROC SURVEYSELECT creates these sampling weights for you.
The following statements demonstrate how you can fit a linear model while incorporating the sample design information (stratification):
title1 'Ice Cream Spending Analysis'; title2 'Stratified Simple Random Sample Design'; proc surveyreg data=IceCream total=StudentTotals; strata Grade /list; class Kids; model Spending = Income Kids / solution anova; weight Weight; run;
Comparing these statements to those in the section 'Simple Random Sampling' on page 4365, you can see how the TOTAL= StudentTotals option replaces the previous TOTAL=4000 option.
The STRATA statement specifies the stratification variable Grade . The LIST option in the STRATA statement requests that the stratification information be included in the output. The WEIGHT statement specifies the weight variable.
Figure 71.4 summarizes the data information, the sample design information, and the fit information. Note that, due to the stratification, the denominator degrees of freedom for F tests and t tests is 37, which is different from the analysis in Figure 71.1.
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Ice Cream Spending Analysis Stratified Simple Random Sample Design The SURVEYREG Procedure Regression Analysis for Dependent Variable Spending Data Summary Number of Observations 40 Sum of Weights 4000.0 Weighted Mean of Spending 9.14130 Weighted Sum of Spending 36565.2 Design Summary Number of Strata 3 Fit Statistics R-square 0.8219 Root MSE 2.4185 Denominator DF 37
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Figure 71.4: Summary of the Regression
For each stratum, Figure 71.5 displays the value of identifying variables, the number of observations (sample size), the total population size , and the calculated sampling rate or fraction.
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Ice Cream Spending Analysis Stratified Simple Random Sample Design The SURVEYREG Procedure Regression Analysis for Dependent Variable Spending Stratum Information Stratum Population Sampling Index Grade N Obs Total Rate 1 7 20 1824 1.10% 2 8 9 1025 0.88% 3 9 11 1151 0.96% Class Level Information Class Variable Levels Values Kids 4 1 2 3 4
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Figure 71.5: Stratification and Classification Information
Figure 71.6 displays the ANOVA table for the regression and tests for the significance of model effects under the stratified sample design. The Income effect is strongly significant, while the Kids effect is not significantatthe5%level.
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Ice Cream Spending Analysis Stratified Simple Random Sample Design The SURVEYREG Procedure Regression Analysis for Dependent Variable Spending Tests of Model Effects Effect Num DF F Value Pr > F Model 4 124.85 <.0001 Intercept 1 150.95 <.0001 Income 1 326.89 <.0001 Kids 3 0.99 0.4081 NOTE: The denominator degrees of freedom for the F tests is 37.
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Figure 71.6: Testing Effects
The regression coefficient estimates for the stratified sample, along with their standard errors and associated t tests, are displayed in Figure 71.7.
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Ice Cream Spending Analysis Stratified Simple Random Sample Design The SURVEYREG Procedure Regression Analysis for Dependent Variable Spending Estimated Regression Coefficients Standard Parameter Estimate Error t Value Pr > t Intercept 26.086882 2.44108058 10.69 <.0001 Income 0.776699 0.04295904 18.08 <.0001 Kids 1 0.888631 1.07000634 0.83 0.4116 Kids 2 1.545726 1.20815863 1.28 0.2087 Kids 3 0.526817 1.32748011 0.40 0.6938 Kids 4 0.000000 0.00000000 . . NOTE: The denominator degrees of freedom for the t tests is 37. Matrix X'WX is singular and a generalized inverse was used to solve the normal equations. Estimates are not unique.
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Figure 71.7: Regression Coefficients
You can request other statistics and tests using PROC SURVEYREG. You can also analyze data from a more complex sample design. The remainder of this chapter provides more detailed information.
Output Data Set
PROC SURVEYREG uses the Output Delivery System (ODS) to create output data sets. This is a departure from older SAS procedures that provide OUTPUT statements for similar functionality. For more information on ODS, see Chapter 14, 'Using the Output Delivery System.'
For example, to save the 'ParameterEstimates' table (Figure 71.7) in the previous section in an output data set, you use the ODS OUTPUT statement as follows :
title1 'Ice Cream Spending Analysis'; title2 'Stratified Simple Random Sample Design'; proc surveyreg data=IceCream total=StudentTotals; strata Grade /list; class Kids; model Spending = Income Kids / solution; weight Weight; ods output ParameterEstimates = MyParmEst; run;
The statement
ods output ParameterEstimates = MyParmEst;
requests that the 'ParameterEstimates' table that appears in Figure 71.7 be placed in a SAS data set named MyParmEst .
The PRINT procedure displays observations of the data set MyParmEst :
proc print data=MyParmEst; run;
Figure 71.8 displays the observations in the data set MyParmEst .
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Ice Cream Spending Analysis Stratified Simple Random Sample Design OBS Parameter Estimate StdErr DenDF tValue Probt 1 Intercept 26.086882 2.44108058 37 10.69 <.0001 2 Income 0.776699 0.04295904 37 18.08 <.0001 3 Kids 1 0.888631 1.07000634 37 0.83 0.4116 4 Kids 2 1.545726 1.20815863 37 1.28 0.2087 5 Kids 3 0.526817 1.32748011 37 0.40 0.6938 6 Kids 4 0.000000 0.00000000 37 . .
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Figure 71.8: The Data Set MyParmEst
The section 'ODS Table Names' on page 4394 gives the complete list of the tables produced by PROC SURVEYREG.
