Adjusting for nonignorable nonresponse using a latent variable mod- eling approach

Nonresponse is present in almost all surveys and can severely bias estimates. It is usually distinguished between unit and item nonresponse: in the former, we completely fail to have information from a unit selected in the sample, while in the latter, we observe only part of the information on the selected unit. Unit nonresponse is usually dealt with by reweighting: each unit selected in the sample has associated a sampling weight and an unknown response probability; the initial sampling weight is multiplied by the inverse of estimated response probabilities. Item nonresponse is usually dealt with by imputation. By noting that for a particular survey variable, we just have observed and unobserved values, in this work we exploit the connection between unit and item nonresponse. Response probabilities are then estimated by using a logistic regression with a latent covariate that measures such "will to respond" and that can explain part of the unknown behaviour of a unit to participate in the survey. The latent covariate is estimated using latent trait models. Such approach is particularly relevant for sensitive items and, therefore, can handle non-ignorable nonresponse. Auxiliary information known for both respondents and nonrespondents can be included either in the latent variable model or in the logistic model. The approach can be also used when auxiliary information is not available, and we analyze here this case. The theoretical properties of the proposed estimators are sketched and simulations studies are conducted to illustrate their finite size sample performance.