Estimation under mode effects and proxy surveys, accounting for non-ignorable nonresponse

We propose a new, model-based methodology to address two major problems in survey sampling: The first problem is known as mode effects, under which responses of sampled units possibly depend on the mode of response, whether by internet, telephone, personal interview, etc. The second problem is of proxy surveys, whereby sampled units respond not only about themselves but also for other sampled. For example, in many familiar household surveys, one member of the household provides information for all other members, possibly with measurement errors. Ignoring the existence of mode effects and/or possible measurement errors in proxy surveys could result in possible bias in point estimators and subsequent inference. Our approach accounts also for nonignorable nonresponse. We illustrate the proposed methodology by use of simulation experiments and real sample data, with known true population values.