An Investigation of Raking to Improve Capture-Recapture Estimates of Population Size

Keywords: raking, iterative proportional fitting, capture-recapture estimation

Abstract: Consider a population in which individuals are cross-classified with respect to demographic and geographic categories. A census is conducted in which individuals are "captured" with probabil- ities that are (hopefully) relatively constant within demographic categories. The census is followed by a random survey in which individuals are "recaptured" independently of the census. Using the two counts, capture-recapture estimates of the demographic category populations are obtained. The population of a geographic entity is estimated by summing demographic adjustment factors (capture-recapture estimate divided by census count) across all individuals captured by the census in the entity. We describe the use of raking, also known as iterative proportional fitting, as a method for smoothing adjustment factors, and evaluate several formulations of raking on data from the 1990 U.S. decennial census.