Include all design information as predictors in your regression model, then postratify if necessary. No need to include survey weights: the information that goes into the weights will be used in any poststratification that is done.

David Kaplan writes: I have a question that comes up often when working with people who are analyzing large scale educational assessments such as NAEP or PISA. They want to do some kind of multilevel analysis of an achievement outcome such as mathematics ability predicted by individual and school level variables. The files contain the …