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A Bayesian Approach to Linking a Survey and a Census via Small Areas

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  • Balgobin Nandram

    (Department of Mathematical Sciences, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA)

Abstract

We predict the finite population proportion of a small area when individual-level data are available from a survey and more extensive household-level (not individual-level) data (covariates but not responses) are available from a census. The census and the survey consist of the same strata and primary sampling units (PSU, or wards) that are matched, but the households are not matched. There are some common covariates at the household level in the survey and the census and these covariates are used to link the households within wards. There are also covariates at the ward level, and the wards are the same in the survey and the census. 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 non-sampled wards. This is accommodated by a multinomial-Dirichlet–Dirichlet model, a three-stage hierarchical Bayesian model for multinomial counts, as it is necessary to account for heterogeneity among the households. The key theoretical contribution of this paper is to develop a computational algorithm to sample the joint posterior density of the multinomial-Dirichlet–Dirichlet model. Specifically, we obtain samples from the distributions of the proportions for each multinomial cell. The second key contribution is to use two projection procedures (parametric based on the nested error regression model and non-parametric based on iterative re-weighted least squares), on these proportions to link the survey to the census, thereby providing a copy of the census counts. We compare the multinomial-Dirichlet–Dirichlet (heterogeneous) model and the multinomial-Dirichlet (homogeneous) model without household effects via these two projection methods. An example of the second Nepal Living Standards Survey is presented.

Suggested Citation

  • Balgobin Nandram, 2021. "A Bayesian Approach to Linking a Survey and a Census via Small Areas," Stats, MDPI, vol. 4(2), pages 1-20, June.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:2:p:31-528:d:571875
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    References listed on IDEAS

    as
    1. Corral Rodas,Paul Andres & Molina,Isabel & Nguyen,Minh Cong, 2020. "Pull Your Small Area Estimates up by the Bootstraps," Policy Research Working Paper Series 9256, The World Bank.
    2. Nandram, Balgobin & Choi, Jai Won, 2010. "A Bayesian Analysis of Body Mass Index Data From Small Domains Under Nonignorable Nonresponse and Selection," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 120-135.
    3. James Dawber & Raymond Chambers, 2019. "Modelling Group Heterogeneity for Small Area Estimation Using M‐Quantiles," International Statistical Review, International Statistical Institute, vol. 87(S1), pages 50-63, May.
    4. Adrijo Chakraborty & Gauri Sankar Datta & Abhyuday Mandal, 2019. "Robust Hierarchical Bayes Small Area Estimation for the Nested Error Linear Regression Model," International Statistical Review, International Statistical Institute, vol. 87(S1), pages 158-176, May.
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