Implied Edit Generation and Error Localization for Ratio and Balancing Edits

The U.S. Census Bureau has developed SPEER software that applies the Fellegi-Holt editing method to economic establishment surveys under ratio edit and a limited form of balancing. It is known that more than 99% of economic data only require these basic forms of edits. If implicit edits are available, then Fellegi-Holt methods have the advantage that they determine the minimal number of fields to change (error localize) so that a record satisfies all edits in one pass through the data. In most situations, implicit edits are not generated because the generation requires days-to-months of computation. In some situations when implicit edits are not available Fellegi-Holt systems use pure integer programming methods to solve the error localization problem directly and slowly (1-100 seconds per record). With only a small subset of the needed implicit edits, the current version of SPEER (Draper and Winkler 1997, upwards of 1000 records per second) applies ad hoc heuristics that finds error-localization solutions that are not optimal for as much as five percent of the edit-failing records. To maintain the speed of SPEER and do a better job of error localization, we apply the Fourier-Motzkin method to generate a large subset of the implied edits prior to error localization. In this paper, we describe the theory, computational algorithms, and results from evaluating the feasibility of this approach.