A design effect measure for calibration weighting in single-stage samples

We propose a model-assisted extension of weighting design-effect measures. We develop a summary-level statistic for different variables of interest, in single-stage sampling and under calibration weight adjustments. Our proposed design effect measure captures the joint effects of a non-epsem sampling design, unequal weights produced using calibration adjustments, and the strength of the association between an analysis variable and the auxiliaries used in calibration. We compare our proposed measure to existing design effect measures in simulations using variables like those collected in establishment surveys and telephone surveys of households.