A model for estimating and imputing nonrespondent census households under sampling for nonresponse follow-up - ARCHIVED

Sampling for nonresponse follow-up (NRFU) was an innovation for U.S. Decennial Census methodology considered for the year 2000. Sampling for NRFU involves sending field enumerators to only a sample of the housing units that did not respond to the initial mailed questionnaire, thereby reducing costs but creating a major small-area estimation problem. We propose a model to impute the characteristics of the housing units that did not respond to the mailed questionnaire, to benefit from the large cost savings of NRFU sampling while still attaining acceptable levels of accuracy for small areas. Our strategy is to model household characteristics using low-dimensional covariates at detailed levels of geography and more detailed covariates at larger levels of geography. To do this, households are first classified into a small number of types. A hierarchical loglinear model then estimates the distribution of household types among the nonsample nonrespondent households in each block. This distribution depends on the characteristics of mailback respondents in the same block and sampled nonrespondents in nearby blocks. Nonsample nonrespondent households can then be imputed according to this estimated household type distribution. We evaluate the performance of our loglinear model through simulation. Results show that, when compared to estimates from alternative models, our loglinear model produces estimates with much smaller MSE in many cases and estimates with approximately the same size MSE in most other cases. Although sampling for NRFU was not used in the 2000 census, our estimation and imputation strategy can be used in any census or survey using sampling for NRFU where units are clustered such that the characteristics of nonrespondents are related to the characteristics of respondents in the same area and also related to the characteristics of sampled nonrespondents in nearby areas.