A 3-SAMPLE MULTIPLE-RECAPTURE APPROACH TO CENSUS POPULATION ESTIMATION WITH HETEROGENEOUS CATCHABILITY

A central assumption in the standard capture-recapture approach to the estimation of the size of a closed population is the homogeneity of t he ''capture'' probabilities. In this article we develop an approach t hat allows for varying susceptibility to capture through individual pa rameters using a variant of the Rasch model from psychological measure ment 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 b e matched with census and Post-Enumeration Survey (PES) data. The mode ls we develop provide a mechanism for separating out the dependence be tween census and PES induced by individual heterogeneity. The resultin g data take the form of an incomplete 2(3) contingency table, and we d escribe 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 indivi duals missed by all three sources involves the log-linear model of no second-order interaction, which is quite plausible under the Rasch mod el. We illustrate the models and their estimation using data from a 19 88 dress-rehearsal study for the 1990 census conducted by the U.S. Bur eau 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.