# The SURVEYREG Procedure

### Example 114.9 Variance Estimate Using the Jackknife Method

This example uses the stratified sample from the section Getting Started: SURVEYREG Procedure to illustrate how to estimate the variances with replication methods.

As shown in the section Stratified Sampling, the sample is saved in the SAS data set `IceCream`. The variable `Grade` that indicates a student’s grade is the stratification variable. 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 variable `Weight` contains sampling weights.

In this example, the procedure uses the jackknife method to estimate the variance, saving the replicate weights that PROC SURVEYREG generates in a SAS data set:

```title1 'Ice Cream Spending Analysis';
title2 'Use the Jackknife Method to Estimate the Variance';
proc surveyreg data=IceCream
varmethod=JACKKNIFE(outweights=JKWeights);
class Kids;
model Spending = Income Kids / solution;
weight Weight;
run;
```

The VARMETHOD=JACKKNIFE option requests the procedure to estimate the variance by using the jackknife method. The OUTWEIGHTS= JKWeights option provides a SAS data set named `JKWeights` that contains the replicate weights used in the computation.

Output 114.9.1 shows the summary of the data and the variance estimation method. There are a total of 40 replicates generated by the procedure.

Output 114.9.1: Variance Estimation Using the Jackknife Method

 Ice Cream Spending Analysis Use the Jackknife Method to Estimate the Variance

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

Variance Estimation
Method Jackknife
Number of Replicates 40

Output 114.9.2 displays the parameter estimates and their standard errors, as well as the tests of model effects that use the jackknife method.

Output 114.9.2: Variance Estimation Using the Jackknife Method

Tests of Model Effects
Effect Num DF F Value Pr > F
Model 4 110.48 <.0001
Intercept 1 133.30 <.0001
Income 1 289.16 <.0001
Kids 3 0.90 0.4525

 Note: The denominator degrees of freedom for the F tests is 37.

Estimated Regression Coefficients
Parameter Estimate Standard
Error
t Value Pr > |t|
Intercept -26.086882 2.58771182 -10.08 <.0001
Income 0.776699 0.04567521 17.00 <.0001
Kids 1 0.888631 1.12799263 0.79 0.4358
Kids 2 1.545726 1.25598146 1.23 0.2262
Kids 3 -0.526817 1.42555453 -0.37 0.7138
Kids 4 0.000000 0.00000000 . .

 Note: The 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.

Output 114.9.3 prints the first 6 observation in the output data set `JKWeights`, which contains the replicate weights.

The data set `JKWeights` contains all the variable in the data set `IceCream`, in addition to the replicate weights variables named `RepWt_1`, `RepWt_2`, ..., `RepWt_40`.

For example, the first observation (student) from stratum `Grade`=7 is deleted to create the first replicate. Therefore, stratum `Grade`=7 is the donor stratum for the first replicate, and the corresponding replicate weights are saved in the variable `RepWt_1`.

Because the first observation is deleted in the first replicate, `RepWt_1`=0 for the first observation. For observations from strata other than the donor stratum `Grade`=7, their replicate weights remain the same as in the variable `Weight`, while the rest of the observations in stratum `Grade`=7 are multiplied by the reciprocal of the corresponding jackknife coefficient, 0.95 for the first replicate.

Output 114.9.3: The Jackknife Replicate Weights for the First 6 Observations

 The Jackknife Weights for the First 6 Obs

Obs Grade Spending Income Kids Prob Weight RepWt_1 RepWt_2 RepWt_3 RepWt_4 RepWt_5 RepWt_6 RepWt_7 RepWt_8 RepWt_9 RepWt_10 RepWt_11 RepWt_12 RepWt_13 RepWt_14 RepWt_15 RepWt_16 RepWt_17 RepWt_18 RepWt_19 RepWt_20 RepWt_21 RepWt_22 RepWt_23 RepWt_24 RepWt_25 RepWt_26 RepWt_27 RepWt_28 RepWt_29 RepWt_30 RepWt_31 RepWt_32 RepWt_33 RepWt_34 RepWt_35 RepWt_36 RepWt_37 RepWt_38 RepWt_39 RepWt_40
1 7 7 39 2 0.010965 91.200 0.000 96.000 91.200 91.200 96.000 96.000 96.000 91.200 91.200 96.000 96.000 91.200 91.200 96.000 96.000 96.000 91.200 91.200 91.200 91.200 91.200 91.200 96.000 96.000 96.000 91.200 91.200 91.200 96.000 96.000 96.000 96.000 91.200 91.200 91.200 96.000 91.200 91.200 96.000 96.000
2 7 7 38 1 0.010965 91.200 96.000 0.000 91.200 91.200 96.000 96.000 96.000 91.200 91.200 96.000 96.000 91.200 91.200 96.000 96.000 96.000 91.200 91.200 91.200 91.200 91.200 91.200 96.000 96.000 96.000 91.200 91.200 91.200 96.000 96.000 96.000 96.000 91.200 91.200 91.200 96.000 91.200 91.200 96.000 96.000
3 8 12 47 1 0.008780 113.889 113.889 113.889 0.000 113.889 113.889 113.889 113.889 128.125 128.125 113.889 113.889 113.889 128.125 113.889 113.889 113.889 113.889 128.125 128.125 113.889 113.889 113.889 113.889 113.889 113.889 113.889 128.125 113.889 113.889 113.889 113.889 113.889 113.889 128.125 128.125 113.889 113.889 113.889 113.889 113.889
4 9 10 47 4 0.009557 104.636 104.636 104.636 104.636 0.000 104.636 104.636 104.636 104.636 104.636 104.636 104.636 115.100 104.636 104.636 104.636 104.636 115.100 104.636 104.636 115.100 115.100 115.100 104.636 104.636 104.636 115.100 104.636 115.100 104.636 104.636 104.636 104.636 115.100 104.636 104.636 104.636 115.100 115.100 104.636 104.636
5 7 1 34 4 0.010965 91.200 96.000 96.000 91.200 91.200 0.000 96.000 96.000 91.200 91.200 96.000 96.000 91.200 91.200 96.000 96.000 96.000 91.200 91.200 91.200 91.200 91.200 91.200 96.000 96.000 96.000 91.200 91.200 91.200 96.000 96.000 96.000 96.000 91.200 91.200 91.200 96.000 91.200 91.200 96.000 96.000
6 7 10 43 2 0.010965 91.200 96.000 96.000 91.200 91.200 96.000 0.000 96.000 91.200 91.200 96.000 96.000 91.200 91.200 96.000 96.000 96.000 91.200 91.200 91.200 91.200 91.200 91.200 96.000 96.000 96.000 91.200 91.200 91.200 96.000 96.000 96.000 96.000 91.200 91.200 91.200 96.000 91.200 91.200 96.000 96.000