Handling nonignorable nonresponse using generalized calibration with latent variables

Calibration weighting has been usefully employed to adjust for unit nonresponse. Generalized calibration allows to distinguish among auxiliary variables between those that are useful to model unit nonresponse (instrumental or model variables) and those that are used in the calibration constraints (calibration variables). Since model variables need only be known on the respondents, generalized calibration offers a particularly useful tool to deal with nonignorable nonresponse. Response to a survey is the outcome of a complex process that involves several aspects: we assume that a part (or all) of such a process may be measured by unobservable variables. Latent variable models can be employed to extract either continuous constructs (latent trait models) or categorical ones (latent class models) from a set of dichotomous/ordered manifest variables. We propose to use such constructs as instrumental variables in the generalized calibration procedure. This allows to include variables of interest among the set of manifest variables. The properties of the proposed methodology are illustrated, then it is tested on a series of simulation studies and finally applied to adjust estimates from the Italian Survey of Households Income and Wealth.