Pseudo Bayesian Mixed Models under Informative Sampling

Savitsky Terrance D. () and Williams Matthew R. ()
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Savitsky Terrance D.: U.S. Bureau of Labor Statistics, Office of Survey Methods Research, 1669 Gales St NE, Washington D.C., 20002, U.S.A.
Williams Matthew R.: RTI International, 3040 East Cornwallis Road, Research Triangle Park, North Carolina, 27709-2194, U.S.A.

Journal of Official Statistics, 2022, vol. 38, issue 3, 901-928

Abstract: When random effects are correlated with survey sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no longer produces asymptotically unbiased inference. We construct a weight-exponentiated formulation for the random effects distribution that achieves approximately unbiased inference for generating hyperparameters of the random effects. We contrast our approach with frequentist methods that rely on numerical integration to reveal that the pseudo Bayesian method achieves both unbiased estimation with respect to the sampling design distribution and consistency with respect to the population generating distribution. Our simulations and real data example for a survey of business establishments demonstrate the utility of our approach across different modeling formulations and sampling designs. This work serves as a capstone for recent developmental efforts that combine traditional survey estimation approaches with the Bayesian modeling paradigm and provides a bridge across the two rich but disparate sub-fields.

Keywords: Labor force dynamics; Markov chain Monte Carlo; pseudo-posterior distribution; survey sampling; weighted likelihood (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:offsta:v:38:y:2022:i:3:p:901-928:n:4

DOI: 10.2478/jos-2022-0039

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