Imagine a (reasonably large) household survey where all persons in every household have been questioned. For the purpose of microsimulation, this survey needs to be expanded to a full population. In a first step, weights are attached to each observation so that external control totals are obeyed (calibration).
If we only have control totals that describe how many households of this-and-that type are in a zone, we can use IPF (also known as raking) which gives a maximum-likelihood estimate of the weights. Minimizing the relative entropy is equivalent to raking/IPF. EDIT: But what if we have control totals at person and household level? Like, telling us how many households of which type and how many persons of which sex/age/education level/... there are. I was unable to find a "standard" approach here.
Is raking/IPF the "correct" approach from a statistical point of view? Are there other options? What would be, from a statistical point of view, the most reasonable approach to calibrate the weights in the presence of control totals at household and person level?
See the original question for more context. (It was probably too big, I'm splitting it into parts.)