A Three-Sample Multiple-Recapture Approach to Census Population Estimation with Heterogeneous Catchability

Abstract

Abstract A central assumption in the standard capture-recapture approach to the estimation of the size of a closed population is the homogeneity of the “capture” probabilities. In this article we develop an approach that allows for varying susceptibility to capture through individual parameters using a variant of the Rasch model from psychological measurement situations. Our approach requires an additional recapture. In the context of census undercount estimation, this requirement amounts to the use of a second independent sample or alternative data source to be matched with census and Post-Enumeration Survey (PES) data. The models we develop provide a mechanism for separating out the dependence between census and PES induced by individual heterogeneity. The resulting data take the form of an incomplete 23 contingency table, and we describe how to estimate the expected values of the observable cells of this table using log-linear quasi-symmetry models. The projection of these estimates onto the unobserved cell corresponding to those individuals missed by all three sources involves the log-linear model of no second-order interaction, which is quite plausible under the Rasch model. We illustrate the models and their estimation using data from a 1988 dress-rehearsal study for the 1990 census conducted by the U.S. Bureau of the Census, which explored the use of administrative data as a supplement to the PES. The article includes a discussion of extensions and related models.