Some of this work is in early stages, and other work is more advanced. We make several recommendations for research to solidify and further advance these lines of development.
The need for nonresponse adjustment arises because probability samples, in which all units have a known, positive probability of selection, require complete responses. Without other non-sampling errors, estimators for probability samples are approximately design-unbiased, consistent, and measurable. Base weights, or inverse probability selection weights, can be used to implement standard estimators.
One possible simple estimator is the ratio mean, which is approximately unbiased and consistent for the population mean:
with di equal to the inverse of the probability of selection. If some of the sample units do not respond (unit nonresponse), and the estimator is unchanged, then the estimator may be biased:
The bias can be expressed in two ways:
(1) A deterministic framework assumes the population contains a stratum of respondents and a stratum of nonrespondents. Let the population means in the two strata be and , respectively. The respondent stratum is R percent of N, and the bias of the unadjusted estimator is
In the deterministic view, the bias arises when the means of the respondents and of the nonrespondents differ.
(2) A stochastic framework assumes every unit in the population has some non-zero probability of responding (its response propensity). The bias of the unadjusted estimator is
1The discussion of nonresponse weighting adjustment methods is abstracted from the presentation by Michael Brick at the panel’s workshop (Brick, 2011).