Item Imputation with the Discrete Edit System

The Fellegi-Holt algorithm (Fellegi and Holt 1976) provides a framework for item imputation by identifying for each record with one or more edit failures a minimal set of fields that must be imputed in order to satisfy a cohesive set of edits. The set of fields is minimal in the sense that there exists at least one joint value for the fields in the set such that, when this joint value is substituted, it results in a record with no edit failure and there does not exist a smaller set of fields that also provides an edit solution. In the paper, we develop an imputation strategy based on a framework similar to FellegiHolt. The input of the imputation process consists of a quasi-minimal set of fields for each record that fails the edits, in addition to distributional information on the fields of the records not failing the edits. The goal of the paper is to show how DISCRETE, an edit-impute system developed at the Census Bureau, process this distributional information to retrieve joint values for a set of fields in such a way that: first, these joint values resolve all the edit conflicts, and second the solution provided is optimal relative to a decision rule based on a likelihood function. In other words, we show how DISCRETE seeks to resolve edit conflicts with a solution that is minimal in the Fellegi-Holt sense, but also with a solution that is probable in reference to a likelihood function.