A Validation of R-Indicators as a Measure of the Risk of Bias using Data from a Nonresponse Follow-Up Survey

R-indicators are increasingly used as nonresponse bias indicators. However, their effectiveness depends on the auxiliary data used in their estimation. Because of this, it is not always clear for practitioners what the magnitude of the R-indicator implies for bias in other survey variables, or how adjustment on auxiliary variables will affect it. In this article, we investigate these potential limitations of R-indicators in a case study using data from the Swiss European Social Survey (ESS5), which included a nonresponse follow-up (NRFU) survey. First, we analyse correlations between estimated response propensities based on auxiliary data from the register-based sampling frame, and responses to survey questions also included in the NRFU. We then examine how these relate to bias detected by the NRFU, before and after adjustment, and to predictions of the risk of bias provided by the R-indicator. While the results lend support for the utility of R-indicators as summary statistics of bias risk, they suggest a need for caution in their interpretation. Even where auxiliary variables are correlated with target variables, more bias in the former (resulting in a larger R-indicator) does not automatically imply more bias in the latter, nor does adjustment on the former necessarily reduce bias in the latter.