Two-Phase Sampling and Weighting

Non-response or other missingness may be occurred in various forms. In this paper, we consider unit non-response, and hence make attempts for adjustments by appropriate weighting. Our special exercise is concerned a two-phase sampling case so that, first, a large sample survey has been conducted with a rather general questionnaire. In the end of this face-to-face contact the interviewer has asked whether a respondent is willing to participate in the second step survey with a very detailed questionnaire concentrating on one of the themes of this initial survey. This procedure leads to the three missingness mechanisms. First there is nonresponse to the initial survey, next there is missingness due to voluntariness of the respondents to participate in the second survey, and finally, it is expected that some more missingness occurs although these volunteers say to be willing to participate in the second survey. Our problem is now how to weight as correctly as possible the second survey respondents so that the results from this survey are reasonable. This paper first analyses missingness differences in these 3 steps using a Finnish data set, and then suggests a weighting technique that uses both the classic methods, that is, post-stratification and calibration, but our main interest lies in a redesign of the response propensity modelling method.