Weighting for two-phase surveyed data

Missingness may occur in various forms. In this paper, we consider unit non-response, and hence make attempts for adjustments by appropriate weighting. Our empirical case concerns two-phase sampling so that first, a large sample survey was conducted using a fairly general questionnaire. At the end of this contact the interviewer asked whether the respondent was willing to participate in the second phase survey with a more detailed questionnaire concentrating on some themes of the first survey. This procedure leads to three missingness mechanisms. Our problem is how to weight the second survey respondents as correctly as possible so that the results from this survey are consistent with those obtained with the first phase survey. The paper first analyses missingness differences in these three steps using a human survey dataset, and then compares different weighting approaches. Our recommendation is that all available auxiliary data should have been used in the best way. This works well with a mixture of the two classic methods that first exploits response propensity weighting and then calibrates these weights to the known population distributions.