I favour the approach the simplified approach outlined here because it requires only small sample sizes and can be used to produce local estimates.

Other approaches (e.g. this one are available and these work OK with large sample surveys (e.g. DHS). I find them to be a bit messy and overcomplicated. The need for a large sample size makes them weak on the "place" dimensions as you may have to limit the spatial granularity of your analysis to large areas. This is probably all you can do with DHS survey data anyway because of the sample design.

I hope this is of some use.

Dear Anon
Could you share more details on what you plan to investigate in the data analysis, e.g. what is the research question(s)? The ENN (together with LSHTM and Save the Children) is currently finalising a DHS data analysis investigating acute malnutrition in infants less than 6 months. Many thanks, Marie