PROC SURVEYPHREG uses the Taylor series method or replication (resampling) methods to estimate sampling errors of estimators that are based on complex sample designs (Fuller; 1975; Särndal, Swensson, and Wretman; 1992; Wolter; 1985; Rust; 1985; Dippo, Fay, and Morganstein; 1984; Rao and Shao; 1999, 1996; and Binder 1992). You can use the VARMETHOD= option in the PROC statement to specify the variance estimation method. By default, PROC SURVEYPHREG uses the Taylor series method.

However, replication methods have recently gained popularity for estimating variances in complex survey data analysis. One reason for this popularity is the relative simplicity of replication-based estimates, especially for nonlinear estimators; another is that modern computational capacity has made replication methods feasible for practical survey analysis.

Replication methods draw multiple replicates (also called subsamples) from a full sample according to a specific resampling scheme. The most commonly used resampling schemes are the balanced repeated replication (BRR) method and the jackknife method. For each replicate, the original weights are modified for the PSUs in the replicates to create replicate weights. The parameters of interest are estimated by using the replicate weights for each replicate. Then the variances of parameters of interest are estimated by the variability among the estimates derived from these replicates. The procedure automatically creates replicate weights based on the replication method you specify; alternatively you can use the REPWEIGHTS statement to provide your own replicate weights for variance estimation.

The following sections provide details about how the variance-covariance matrix of the estimated regression coefficients is estimated for each variance estimation method.