Domain analysis refers to the computation of statistics for domains (subpopulations). Formation of subpopulations can be unrelated to the sample design, and so the domain sample sizes can actually be random variables. Domain analysis takes this variability into account to compute variance estimates for estimated model parameters. Domain analysis is also known as subgroup analysis, subpopulation analysis, and subdomain analysis. For more information about domain analysis, see Lohr (2009), Särndal, Swensson, and Wretman (1992), and Cochran (1977).

To request domain analysis with PROC SURVEYPHREG, use the DOMAIN statement. If your domains are formed by more than one variable, you can specify DomainVariable_1 * DomainVariable_2 in the DOMAIN statement. If you use the DOMAIN statement, the procedure performs separate analyses for all domains, in addition to the overall analysis.

Including the domain variables in a DOMAIN statement request provides a different analysis from that obtained by using a BY statement, which provides completely separate analyses of the BY groups. The BY statement can also be used to analyze the data set by subgroups, but it is critical to note that this does not account for random sample sizes that often occur for domain analyses. The BY statement is appropriate only when the number of units in each subgroup is known with certainty. For example, the BY statement can be used to obtain stratum level estimates when you have fixed sample sizes for the strata. When the subgroup sample size is random, include the domain variables in DOMAIN statement.