Generalised calibration with latent variables for the treatment of unit nonresponse in sample surveys

Sample surveys may suffer from nonignorable unit nonresponse. This happens when the decision of whether or not to participate in the survey is correlated with variables of interest; in such a case, nonresponse produces biased estimates for parameters related to those variables, even after adjustments that account for auxiliary information. This paper presents a method to deal with nonignorable unit nonresponse that uses generalised calibration and latent variable modelling. Generalised calibration enables to model unit nonresponse using a set of auxiliary variables (instrumental or model variables), that can be different from those used in the calibration constraints (calibration variables). We propose to use latent variables to estimate the probability to participate in the survey and to construct a reweighting system incorporating such latent variables. The proposed methodology is illustrated, its properties discussed and tested on two simulation studies. Finally, it is applied to adjust estimates of the finite population mean wealth from the Italian Survey of Household Income and Wealth.