PROC SURVEYMEANS: Balanced Repeated Replication (BRR) Method :: SAS/STAT(R) 9.2 User's Guide, Second Edition

The SURVEYMEANS Procedure

Balanced Repeated Replication (BRR) Method

The balanced repeated replication (BRR) method requires that the full sample be drawn by using a stratified sample design with two primary sampling units (PSUs) per stratum. Let $\text{[math]}$ be the total number of strata. The total number of replicates $\text{[math]}$ is the smallest multiple of 4 that is greater than $\text{[math]}$ . However, if you prefer a larger number of replicates, you can specify the REPS=number option. If a $\text{[math]}$ Hadamard matrix cannot be constructed, the number of replicates is increased until a Hadamard matrix becomes available.

Each replicate is obtained by deleting one PSU per stratum according to the corresponding Hadamard matrix and adjusting the original weights for the remaining PSUs. The new weights are called replicate weights.

Replicates are constructed by using the first $\text{[math]}$ columns of the $\text{[math]}$ Hadamard matrix. The $\text{[math]}$ th ( $\text{[math]}$ ) replicate is drawn from the full sample according to the $\text{[math]}$ th row of the Hadamard matrix as follows:

If the $\text{[math]}$ th element of the Hadamard matrix is $\text{[math]}$ , then the first PSU of stratum $\text{[math]}$ is included in the $\text{[math]}$ th replicate and the second PSU of stratum $\text{[math]}$ is excluded.
If the $\text{[math]}$ th element of the Hadamard matrix is $\text{[math]}$ , then the second PSU of stratum $\text{[math]}$ is included in the $\text{[math]}$ th replicate and the first PSU of stratum $\text{[math]}$ is excluded.

The replicate weights of the remaining PSUs in each half sample are then doubled to their original weights. For more details about the BRR method, see Wolter (1985) and Lohr (1999).

By default, an appropriate Hadamard matrix is generated automatically to create the replicates. You can request that the Hadamard matrix be displayed by specifying the VARMETHOD=BRR(PRINTH) method-option. If you provide a Hadamard matrix by specifying the VARMETHOD=BRR(HADAMARD=) method-option, then the replicates are generated according to the provided Hadamard matrix.

Suppose that $\text{[math]}$ is a population parameter of interest. Let $\text{[math]}$ be the estimate from the full sample for $\text{[math]}$ . Let $\text{[math]}$ be the estimate from the $\text{[math]}$ th replicate subsample by using replicate weights. PROC SURVEYMEANS estimates the variance of $\text{[math]}$ by

$\text{[math]}$

with $\text{[math]}$ degrees of freedom, where $\text{[math]}$ is the number of strata.

You can use the VARMETHOD=BRR(OUTWEIGHTS=) method-option to save the replicate weights into a SAS data set.

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