Weight Smoothing for Generalized Linear Models Using a Laplace Prior

Xia Xi () and Elliott Michael R. ()
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Xia Xi: Dept. of Biostatistics, University of Michigan School of Public Health, 1415 Washington Heights, Ann Arbor, MI 48109, USA.
Elliott Michael R.: Dept. of Biostatistics, University of Michigan School of Public Health, 1415 Washington Heights, Ann Arbor, MI 48109, USA. Survey Methodology Program, Institute for Social Research, University of Michigan, 426 Thompson St., Ann Arbor, MI 48109, USA.

Journal of Official Statistics, 2016, vol. 32, issue 2, 507-539

Abstract: When analyzing data sampled with unequal inclusion probabilities, correlations between the probability of selection and the sampled data can induce bias if the inclusion probabilities are ignored in the analysis. Weights equal to the inverse of the probability of inclusion are commonly used to correct possible bias. When weights are uncorrelated with the descriptive or model estimators of interest, highly disproportional sample designs resulting in large weights can introduce unnecessary variability, leading to an overall larger mean square error compared to unweighted methods.We describe an approach we term ‘weight smoothing’ that models the interactions between the weights and the estimators as random effects, reducing the root mean square error (RMSE) by shrinking interactions toward zero when such shrinkage is allowed by the data. This article adapts a flexible Laplace prior distribution for the hierarchical Bayesian model to gain a more robust bias-variance tradeoff than previous approaches using normal priors. Simulation and application suggest that under a linear model setting, weight-smoothing models with Laplace priors yield robust results when weighting is necessary, and provide considerable reduction in RMSE otherwise. In logistic regression models, estimates using weight-smoothing models with Laplace priors are robust, but with less gain in efficiency than in linear regression settings.

Keywords: Weight trimming; winsorization; Bayesian finite population inference; Hierarchical models (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:offsta:v:32:y:2016:i:2:p:507-539:n:14

DOI: 10.1515/jos-2016-0026

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