Does the use of calibration/post-stratification imply that the sampling strategy/stratification/individual selection probabilities can be ignored altogether?
In a survey reweighting exercise, I have population totals for a complete cross-classification of four attributes: country, age, sex, and work status. EDIT: The sampling scheme is stratified by country (about the same number of respondents per country), and within each country stratified by age and sex (very roughly uniform). The work status is not part of the sampling stratification.
My task is to produce generic weights that can be used for identifying interactions between variables (stratification-response and response-response). Estimation of population means or totals might be another application. (At least that's what I understand. To be honest, I don't really know the application -- how much does it matter?)
Question: How will the calibrated weights be affected if information on the sampling strategy is added to the calibration procedure, e.g. in the form of prior weights? Is it a problem when for some combinations of categories there are only very few respondents?
Question related to the practical exercise: https://stats.stackexchange.com/q/29132/6432