Summary: We consider surveys with one or more callbacks and use a series of logistic regressions to model the probabilities of nonresponse at first contact and subsequent callbacks. These probabilities are allowed to depend on covariates as well as the categorical variable of interest and so the nonresponse mechanism is nonignorable. Explicit formulae for the score functions and information matrices are given for some important special cases to facilitate implementation of the method of scoring for obtaining maximum likelihood estimates of the model parameters. For estimating finite population quantities, we suggest the imputation and prediction approaches as alternatives to weighting adjustment.
Simulation results suggest that the proposed methods work well in reducing the bias due to nonresponse. In our study, the imputation and prediction approaches perform better than weighting adjustment and they continue to perform quite well in simulations involving misspecified response models.