The SURVEYPHREG Procedure
Variance Ratios and Standard Error Ratios
PROC SURVEYPHREG provides options to compute the following variance ratios and standard error ratios:
If you specify the VARRATIO=MODEL option, then the procedure computes the variance ratio of the estimated regression parameter
as 
, where 
, the estimated variance of , uses the complete design information and 
is the jth diagonal element of the observed information matrix 
. -
If you specify the VARRATIO=IND option, then the procedure computes the variance ratio of the estimated regression parameter
as 
, where , the estimated variance of , uses the complete design information and 
is the jth diagonal element of 
. is the sandwich variance estimator, which ignores the strata and the clusters and is computed as 
where
are the weighted score residuals, f is the overall sampling fraction, and n is the number of observation units. The three sums are over the observation units (j) across the PSUs (i) and the strata (h). -
If you specify the VARRATIO=SRSWR option, then the procedure computes the variance ratio of the estimated regression parameter
as 
, where , the estimated variance of , uses the complete design information and 
is the jth diagonal element of 
. is given by 
where
is the observation weight for unit (h, i, j) and n is the number of observation units. The three sums are over the observation units (j) across the PSUs (i) and the strata (h).
The matrix 
is often called the generalized design effect matrix (Rao, Scott, and Skinner 1998). -
If you specify the VARRATIO=SRSWOR option, then the procedure computes the variance ratio of the estimated regression parameter
as 
, where , the estimated variance of , uses the complete design information and 
is the jth diagonal element of 
. is given by 
where
is the observation weight for unit (h, i, j), f is the overall sampling fraction, and n is the number of observation units. The three sums are over the observation units (j) across the PSUs (i) and the strata (h).
For Taylor series or bootstrap variance estimation, PROC SURVEYPHREG determines the value of f, the overall sampling fraction, based on the RATE= or TOTAL= option. If you do not specify either of these options, PROC SURVEYPHREG assumes that the value of f is negligible and does not use a finite population correction in the analysis. If you specify RATE=value, PROC SURVEYPHREG uses value as the overall sampling fraction f. If you specify TOTAL=value, PROC SURVEYPHREG computes f as the ratio of the number of PSUs in the sample to the specified total.
If you specify stratum sampling rates by using the RATE=SAS-data-set option, then PROC SURVEYPHREG computes stratum totals based on these stratum sampling rates and the number of sample PSUs in each stratum. The procedure sums the stratum totals to form the overall total and then computes f as the ratio of the number of sample PSUs to the overall total. Alternatively, if you specify stratum totals with the TOTAL=SAS-data-set option, then PROC SURVEYPHREG sums these totals to compute the overall total. The overall sampling fraction f is then computed as the ratio of the number of sample PSUs to the overall total.
The replication methods do not use the finite population correction factor 
in the denominator.
Standard error ratios are computed as the square root of the variance ratios.