Estimation with probability edited survey data under nonresponse

Probabilistic editing has been introduced to enable valid inference using established survey sampling theory in situations when some of the collected data points may have measurement errors and are therefore submitted to an editing process. To reduce the editing effort and avoid over-editing, in current practice selective editing is most often used, which is a form of editing that limits the edit checks to those potential errors that, if indeed in error, are likely to have the biggest impact on estimates to be produced. However, selective editing is not grounded in probability theory associated with survey sampling, and cannot provide expressions for point and variance estimates that account for the uncertainties introduced by selective editing. In the spirit of the total survey error paradigm, this paper extends the previous work on probabilistic editing by proposing an estimation procedure that provides valid inference when two kinds of nonsampling error are simultaneously present, in addition to the sampling error: the measurement error, requiring an editing step, and the practically unavoidable nonresponse error which also needs to be taken into account when producing unbiased estimates. In a three-phase selection setup, bias due to measurement error is estimated through probabilistic editing while weight adjustment employing auxiliary information is used to deal with nonresponse. An estimator based on calibration for nonresponse and corrected for bias due to measurement error is introduced. Its theoretical variance and an estimator of the variance are derived. A simulation study illustrates the three-phase selection setup and the practical performance of the derived point and variance estimators.