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Pseudo Bayesian Mixed Models under Informative Sampling

Author

Listed:
  • 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.)

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.

Suggested Citation

  • Savitsky Terrance D. & Williams Matthew R., 2022. "Pseudo Bayesian Mixed Models under Informative Sampling," Journal of Official Statistics, Sciendo, vol. 38(3), pages 901-928, September.
  • Handle: RePEc:vrs:offsta:v:38:y:2022:i:3:p:901-928:n:4
    DOI: 10.2478/jos-2022-0039
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    References listed on IDEAS

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    1. Lele, Subhash R. & Nadeem, Khurram & Schmuland, Byron, 2010. "Estimability and Likelihood Inference for Generalized Linear Mixed Models Using Data Cloning," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1617-1625.
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