Propensity score adjustment with several follow-ups

Abstract

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 followup 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 followup 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 two methods, one using calibration weighting and the other using a conditional likelihood using a so-called reverse conditional probability. Both methods provides consistent estimates under correct specification of the response model. A limited simulation study is used to compare the estimators. The proposed methods are applied to the real data example in a Korean household survey of employment.

Semiparametric maximum likelihood inference for nonignorable nonresponse with callbacks

“…The regression model is m ( x ; α )= α 0 + α 1 x , which is correct for simulation Model I but incorrect for Model II. From this simulation, we see that when the auxiliary information E[ a ( X )]=0 is used, our method performs better than that of Kim and Im ().…”

“…Table presents the results of a simulation of 2,000 Monte Carlo runs using the setup of Kim and Im () with v =2 and N =600. These results can be compared with those in table 1 of Kim and Im ().…”

“…Table presents the results of a simulation of 2,000 Monte Carlo runs using the setup of Kim and Im () with v =2 and N =600. These results can be compared with those in table 1 of Kim and Im (). We generated y i using Model I: y i =0.8+ x i + ε i and Model II: , where x i ∼Uniform(−2,2) and ε i ∼ N (0,1/2).…”

“…Wood, White, and Hotopf () used a number of failed contact attempts to adjust for nonignorable nonresponse data problems with application to a postal survey of symptoms in Persian Gulf War veterans and other servicemen. Kim and Im () also investigated this problem and proposed method‐of‐moment estimators of the parameters in the response probability.…”

“…In this paper, we consider a similar case discussed by Alho () and Kim and Im () in which for each individual in a survey study, the associated variables consist of a vector of outcome variables that may not be attainable for some individuals and some covariates. As in Kim and Im (), we assume that the covariates were always observed even if the individual failed to respond, and there might be callbacks to nonrespondents. However, the model setups and assumptions of this paper are quite different from theirs.…”