The SURVEYREG Procedure

Notation

For a stratified clustered sample design, observations are represented by an $\text{[math]}$ matrix

$\text{[math]}$

where

$\text{[math]}$ denotes the sampling weight vector
$\text{[math]}$ denotes the dependent variable
$\text{[math]}$ denotes the $\text{[math]}$ design matrix. (When an effect contains only classification variables, the columns of $\text{[math]}$ that correspond this effect contain only 0s and 1s; no reparameterization is made.)
$\text{[math]}$ is the stratum index
$\text{[math]}$ is the cluster index within stratum $\text{[math]}$
$\text{[math]}$ is the unit index within cluster $\text{[math]}$ of stratum $\text{[math]}$
$\text{[math]}$ is the total number of parameters (including an intercept if the INTERCEPT effect is included in the MODEL statement)
$\text{[math]}$ is the total number of observations in the sample

Also, $\text{[math]}$ denotes the sampling rate for stratum $\text{[math]}$ . You can use the TOTAL= or RATE= option to input population totals or sampling rates. See the section Specification of Population Totals and Sampling Rates for details. If you input stratum totals, PROC SURVEYREG computes $\text{[math]}$ as the ratio of the stratum sample size to the stratum total. If you input stratum sampling rates, PROC SURVEYREG uses these values directly for $\text{[math]}$ . If you do not specify the TOTAL= or RATE= option, then the procedure assumes that the stratum sampling rates $\text{[math]}$ are negligible, and a finite population correction is not used when computing variances.