A Bayesian Approach to Combining Information from a Census, a Coverage Measurement Survey, and Demographic Analysis

Abstract

Demographic analysis of data on births, deaths, and migration and coverage measurement surveys that use capture-recapture methods have both been used to assess U.S. Census counts. These approaches have established that unadjusted Census counts are seriously flawed for groups such as young and middle-aged African-American men. There is considerable interest in methods that combine information from the Census, coverage measurement surveys, and demographic information to improve Census estimates of the population. This article describes a number of models that have been proposed to accomplish this synthesis when the demographic information is in the form of sex ratios stratified by age and race. A key difficulty is that methods for combining information require modeling assumptions that are difficult to assess based on fit to the data. We propose some general principles for aiding the choice among alternative models. We then pick a particular model based on these principles and imbed it within a more comprehensive Bayesian model for counts in poststrata of the population. Our Bayesian approach provides a principled solution to the existence of negative estimated counts in some subpopulations; provides for smoothing of estimates across poststrata, reducing the problem of isolated outlying adjustments; allows a test of whether negative cell counts are due to sampling variability or more egregious problems such as bias in Census or coverage measurement survey counts; and can be easily extended to provide estimates of precision that incorporate uncertainty in the estimates from demographic analysis and other sources. The model is applied to data for African-American age 30–49 from the 1990 Census, and results are compared with those from existing methods.

Key Words:

• Gibbs sampling
• Model selection
• Postenumeration survey
• Posterior predictive distribution