A method of weighting adjustment for survey data subject to nonignorable nonresponse

Weighting adjustment is a standard quasi-randomization approach for survey data subject to nonresponse Little (1986). The existing methods are typically based on the assumption that nonresponse is independent of the survey variable conditional to the auxiliary variables used to form the adjustment cells. In this paper we consider nonignorable nonresponse which is independent of certain auxiliary information conditional to the variable of interest. We estimate the size of the sample adjustment cells using a method of moment conditional to the sample. The method relies on only the nonresponse mechanism, and is independent of the sample design. In variance estimation, we evaluate the nonresponse effect on estimation and design, analogously to the concept of design effect. By comparing the nonresponse effects under a nonignorable model against those under an ignorable one, we obtain a means of measuring the effect of nonignorability. We motivate and illustrate our approach for estimation of household composition.