Semiparametric maximum likelihood inference for nonignorable nonresponse with callbacks

摘要

We model the nonresponse probabilities as logistic functions of the outcome variable and other covariates in the survey study with callback. The identification aspect of this callback model is investigated. Semiparametric maximum likelihood estimators of the parameters in the response probabilities are proposed and studied. As a result, an efficient estimator of the mean of the outcome variable is constructed using the estimated response probabilities. Moreover, if a regression model for the conditional mean of the outcome variable given some covariate is available, then we can obtain an even more efficient estimate of the mean of the outcome variable by fitting the regression model using an adjusted least-squares method based on the estimated underlying distributions of the observed values. Simulation results show that the proposed method is more efficient compared with some existing competitors. The method is applied to data from the Singapore Life Panel, a survey of health spending using a population-based sample of individuals aged 50-70 years, where nonresponse may be related to health.