PROC SURVEYMEANS: Fay’s BRR Method :: SAS/STAT(R) 9.2 User's Guide, Second Edition

The SURVEYMEANS Procedure

Fay’s BRR Method

Fay’s method is a modification of the BRR method, and it requires a stratified sample design with two primary sampling units (PSUs) per stratum. The total number of replicates $\text{[math]}$ is the smallest multiple of 4 that is greater than the total number of strata $\text{[math]}$ . However, if you prefer a larger number of replicates, you can specify the REPS= method-option.

For each replicate, Fay’s method uses a Fay coefficient $\text{[math]}$ to impose a perturbation of the original weights in the full sample that is gentler than using only half samples, as in the traditional BRR method. The Fay coefficient $\text{[math]}$ can be optionally set by the FAY = $\text{[math]}$ method-option. By default, $\text{[math]}$ if only the FAY method-option is used without specifying a value for $\text{[math]}$ (Judkins 1990; Rao and Shao 1999). When $\text{[math]}$ , Fay’s method becomes the traditional BRR method. For more details, see Dippo, Fay, and Morganstein (1984), Fay (1984), Fay (1989), and Judkins (1990).

Let $\text{[math]}$ be the number of strata. Replicates are constructed by using the first $\text{[math]}$ columns of the $\text{[math]}$ Hadamard matrix, where $\text{[math]}$ is the number of replicates, $\text{[math]}$ . The $\text{[math]}$ th ( $\text{[math]}$ ) replicate is created 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 full sample weight of the first PSU in stratum $\text{[math]}$ is multiplied by $\text{[math]}$ and that of the second PSU is multiplied by $\text{[math]}$ to obtain the $\text{[math]}$ th replicate weights.
If the $\text{[math]}$ th element of the Hadamard matrix is $\text{[math]}$ , then the full sample weight of the first PSU in stratum $\text{[math]}$ is multiplied by $\text{[math]}$ and that of the second PSU is multiplied by $\text{[math]}$ to obtain the $\text{[math]}$ th replicate weights.

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

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.

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