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Abstract:
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We predict the finite population proportion of a small area when individual-level data are available from a survey and more extensive data (covariates but not responses) are available from a census. The census and the survey consist of the same strata and primary sampling units (PSUs or wards) that are matched, but the households are not matched. Moreover, the covariates in the survey and the census are not all different. Using a two-stage procedure, we study the multinomial counts in the sampled households within the wards and a projection method to infer about the nonsampled wards. This is accommodated by a three-stage hierarchical Bayesian model for multinomial counts as it is necessary to account for heterogeneity among the households. To proceed, we obtain samples from the distributions of the proportions for each multinomial cell, and then we use these samples to do projective inference for the finite population proportions. Using two projection procedures (parametric and nonparametric), we compare the heterogeneous model and a homogeneous model without household effects. An example on the second Nepal Living Standards Survey is presented.
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