<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

Pseudo Bayesian Mixed Models under Informative Sampling

Journal of Official Statistics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Pseudo Bayesian Mixed Models under Informative Sampling"}

When random effects are correlated with survey sample design variables, the usual approach of employing individual survey weights (constructed to be inversely...

Pseudo Bayesian Mixed Models under Informative Sampling

Published Online: Sep 12, 2022

Page range: 901 - 928

Received: Mar 01, 2021

Accepted: Mar 01, 2022

DOI: https://doi.org/10.2478/jos-2022-0039

Keywords
Labor force dynamics, Markov chain Monte Carlo, pseudo-posterior distribution, survey sampling, weighted likelihood

© 2022 Terrance D. Savitsky et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Pseudo Bayesian Mixed Models under Informative Sampling

Published Online: Sep 12, 2022

Page range: 901 - 928

Received: Mar 01, 2021

Accepted: Mar 01, 2022

DOI: https://doi.org/10.2478/jos-2022-0039

KeywordsLabor force dynamics, Markov chain Monte Carlo, pseudo-posterior distribution, survey sampling, weighted likelihood

© 2022 Terrance D. Savitsky et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Labor force dynamics, Markov chain Monte Carlo, pseudo-posterior distribution, survey sampling, weighted likelihood