Multiple Imputation for Nonignorable Item Nonresponse in Complex Surveys Using Auxiliary Margin

TL;DR

This paper introduces a new multiple imputation framework for nonignorable item nonresponse in complex surveys, ensuring plausible estimates and preserving variable associations using auxiliary margins and rejection sampling.

Contribution

It proposes an additive nonignorable model combined with rejection sampling to produce realistic imputed datasets consistent with known margins.

Findings

Framework produces plausible design-based estimates

Maintains associations across variables in imputed data

Effective in stratified sampling simulations

Abstract

We outline a framework for multiple imputation of nonignorable item nonresponse when the marginal distributions of some of the variables with missing values are known. In particular, our framework ensures that (i) the completed datasets result in design-based estimates of totals that are plausible, given the margins, and (ii) the completed datasets maintain associations across variables as posited in the imputation models. To do so, we propose an additive nonignorable model for nonresponse, coupled with a rejection sampling step. The rejection sampling step favors completed datasets that result in design-based estimates that are plausible given the known margins. We illustrate the framework using simulations with stratified sampling.