From the sheet about weighting of ESDS, we know that there are 3 types of weights:

(1) Sample Design or Probability Weights;

(2) Non-response weights ;

(3) Post-stratification weights.

Based on observed variables, one calculate the prob of an observation being included and weight the observation with the inverse of this weight.

Weight (2) is also a type of IPW. However, we use an incomplete set of variables to put observations into different classes and observations in the same class are given the same weight. Thus, we implicitly make an assumption that observations in the same class are of the same characteristic. Of course, this could be wrong.

Weight (3) is just a fequency weight to adjust our sample to represent the real population.

The thing is they normally combine these weights together. As we can see, (1) is like the weight in IPW M-estimtor and (2) is the weight of Richard and Esmeralda. Can we find an optimal way to combine these two weights?? Note that (1) can be continuously vary with observations according to its definition but (2) have to be constant for observations in the same class.

Another point is whether there is a difference between weighting of survey data in general and weighting in a particular study. For example, in a dataset from LFS that we are working on, there are two weights provided. However, "hrrate" is not fully observed and we would like to do IPW M-estimation to take an account of this missingness. So even though the weights provided (pwt03, piwt03) are calculated using non-response weight, we should calculate our own weights and combined them together???