COMBINING CENSUS, DUAL-SYSTEM, AND EVALUATION STUDY DATA TO ESTIMATE POPULATION SHARES

The 1990 census and Post-Enumeration Survey produced census and dual s ystem estimates (DSE) of population by domain, together with an estima ted sampling covariance matrix of the DSE. Estimates of the bias of th e DSE were derived from various PES evaluation programs. Of the three sources, the unadjusted census is the least variable but is believed t o be the most biased, the DSE is less biased but more variable, and th e bias estimates may be regarded as unbiased but are the most variable . This article addresses methods for combining the census, the DSE, an d bias estimates obtained from the evaluation programs to produce accu rate estimates of population shares, as measured by weighted squared- or absolute-error loss functions applied to estimated population share s of domains. Several procedures are reviewed that choose between the census and the DSE using the bias evaluation data or that average the two with weights that are constant across domains. A multivariate hier archical Bayes model is proposed for the joint distribution of the und ercount rates and the biases of the DSE in the various domains. The sp ecification of the model is sufficiently flexible to incorporate prior information on factors likely to be associated with undercount and bi as. When combined with data on undercount and bias estimates, the mode l yields posterior distributions for the true population shares of eac h domain. The performance of the estimators was compared through an ex tensive series of simulations. The hierarchical Bayes procedures are s hown to outperform the other estimators over a wide range of condition s and to be robust against misspecification of the models. The various composite estimators, applied to preliminary data from the 1990 Censu s and evaluation programs. yield similar results that are closer to th e DSE than to the census. Analysis of a revised data set yields qualit atively similar estimates but shows that the revised post-stratificati on improves on the original one.