A stableness of resistance model for nonresponse adjustment with callback data

The survey world is rife with nonresponse and in many situations the missingness mechanism is not at random, which is a major source of bias for statistical inference. Nonetheless, the survey world is rich with paradata that track the data collection process. A traditional form of paradata is callback data that record attempts to contact. Although it has been recognized that callback data are useful for nonresponse adjustment, they have not been used widely in statistical analysis until recently. In particular, there have been a few attempts that use callback data to estimate response propensity scores, which rest on fully parametric models and fairly stringent assumptions. In this paper, we propose a stableness of resistance assumption for identifying the propensity scores and the outcome distribution of interest, without imposing any parametric restrictions. We establish the semiparametric efficiency theory, derive the efficient influence function, and propose a suite of semiparametric estimation methods including doubly robust ones, which generalize existing parametric approaches. We also consider extension of this framework to causal inference for unmeasured confounding adjustment. Application to a Consumer Expenditure Survey dataset suggests an association between nonresponse and high housing expenditures, and reanalysis of Card (1995)'s dataset on the return to schooling shows a smaller effect of education in the overall population than in the respondents.