Propensity score adjustment with several follow-ups

Propensity score weighting adjustment is commonly used to handle unit nonresponse. When the response mechanism is nonignorable in the sense that the response probability depends directly on the study variable, a follow-up sample is commonly used to obtain an unbiased estimator using the framework of two-phase sampling, where the follow-up sample is assumed to respond completely. In practice, the follow-up sample is also subject to missingness. We consider propensity score weighting adjustment for nonignorable nonresponse when there are several follow-ups and the final follow-up sample is also subject to missingness. We propose a method-of-moments estimator for estimating parameters in the response probability. The proposed method can be implemented using the generalized method of moments and a consistent variance estimate can be obtained relatively easily. A limited simulation study shows the robustness of the proposed method. The proposed methods are applied to a Korean household survey of employment.