Handling nonignorable nonresponse with respondent modeling and the SIR algorithm

• Sensitivity to model specification in missing data problems is a serious scientific problem.
• We propose a simulation method using SIR and a respondent model.
• Asymptotic results are given and simulations are performed.
• Results are encouraging and superior to naive methods.
• Proposed methods could be used in applications in many scientific areas.

Handling missing data based on parametric models typically involves computing the conditional expectation of missing data given observed data for nonrespondents. Under a nonignorable missing data mechanism, the conditional distribution requires joint modeling of the study and response variables. A natural way of factoring the model is to use models for the distribution of variables under complete response and for the probability of response. Sensitivity to model specification is a serious scientific problem. Models cannot be validated, however, from missing data, because, by definition, the information needed for validation is missing.In many cases, under assumed models, a Monte Carlo (MC) method can be used to compute the conditional expectation of missing given observed variables. The issue of model specification translates into the questions, how should one generate values from the conditional distribution for nonrespondents? One way to interpret this issue is as the need to specify an imputation method for the missing data.In this paper, we consider a simulation method based on the model for the distribution of respondents together with the Sampling Importance Resampling (SIR) algorithm. The proposed method is shown to be more robust than some current approaches in the sense that assumed models can be verified from respondents. A linearized variance estimation method is also studied. Results from a limited simulation study are presented.