Latent Variable Models for Nonresponse Adjustment and Calibration

Traditional weight adjustments for survey sampling error are often constructed through multiple stages, where design weights are based on the inverse of the probability of selection, and in a separate stage nonresponse adjustments are derived from weighting cells or classes, or based on model-deduced response propensities. More recent efforts by Little and Vartivarian (2003) have advocated the use of propensity models that incorporate both design information, as well as variables that are, ideally, related to both nonresponse and the survey outcome. There is often a third stage of adjustment that involves calibration to known or reliable population totals. It would be useful to incorporate this calibration stage into a propensity model containing the design information and variables related to response behavior. This can be accomplished via a latent constructs that are constrained (by totals or proportions) to the external information being used. By simultaneously estimating the response propensity under calibration and incorporating design variables, additional variance due to adjustment would be minimized.