I have a question about nonresponse weighting in complex sample surveys in multi-stage designs, like say, The US National Comorbidity Survey Replication (NCS-R), the Health and Retirement Study (HRS), or perhaps the most well known NHANES (National Health and Nutrition Examination Survey). I generally understand the concept of nonresponse weighting in simple surveys, but I'm wondering how the non-response weights would work in a multi-stage design, where a household is selected in one stage and then individuals within a household are selected to participate. My questions is: is a non-response weight calculated at the household level (e.g. if the whole household refuses to participate), and then a separate non-response weight calculated for individuals in a selected household who refuse to participate and then a final non-response weight computed by multiplying the household nonresponse weight with the individual within the household nonresponse weight? In other words, are these typically computed:
Final Nonresponse Weight = Household Nonresponse weight x Individual within Household Nonresponse weight
Or do the survey statisticians typically just compute a single nonresponse weight that is simply applied at the respondent level? I was thinking it probably makes sense to compute a household nonresponse weight because you might be interested in estimating household level variables and without the household weight, you wouldn't be able to accurately estimate this (unless you designated and obtained the household level variable from at least one respondent from within the household).
Can anyone provide any insight into how this is done in practice?
Thanks.
