When adjusting for unit nonresponse in a survey, it is common to assume that the response/nonresponse mechanism is a function of variables known either for the entire sample before unit response or at the aggregate level for the frame or population. Often, however, some of the variables governing the response/nonresponse mechanism can only be proxied by variables on the frame while they are measured (more) accurately on the survey itself. For example, an address-based sampling frame may contain area-level estimates for the median annual income and the fraction home ownership in a Census block group, while a household's annual income category and ownership status are reported on the survey itself for the housing units responding to the survey. A relatively new calibration-weighting technique allows a statistician to calibrate the sample using proxy variables while assuming the response/nonresponse mechanism is a function of the analogous survey variables. We will demonstrate how this can be done with data from the Residential Energy Consumption Survey National Pilot, a nationally representative web-and-mail survey of American households sponsored by the U.S. Energy Information Administration.
Calibration weighting for nonresponse with proxy frame variables (so that unit nonresponse can be not missing at random)