We agree that multi-level analysis should include weights at each level. Until Stata 14, multi-level models in Stata could not use weights at all. Beginning with Stata 14, weights (multi-level weights) are allowed and should be used (as in MLwin). The problem is that DHS does not have cluster-level weights. The clusters are sampled with probability proportional to size, within strata. The sizes of the clusters, usually census enumeration areas, are part of the sampling frame, usually the most recent census. The sampling frame is not public information. DHS only has access to it within the country and is not allowed to make a copy of it. Statistical offices typically do not want to share it.

It is conceivable that there is some way to approximate the cluster-level weights or at least to get away from the invalid assumption that the first stage sampling probabilities are the same for all clusters. We will look into this. Thanks for raising the issue.