Hierarchical Model Selection Using a Benchmark Discrepancy
نویسندگان
چکیده
In the context of small area estimation, hierarchical Bayesian (HB) models are often proposed to produce more reliable estimators of small area quantities than direct estimates, such as design-based survey estimators. A method that benchmarks HB estimates with respect to higher level direct estimates and measures the relative inflation in the posterior mean square error of distributions due to benchmarking is developed to evaluate the performance of hierarchical models. The benchmarked hierarchical Bayesian posterior predictive model comparison method is shown to be able to select proper models effectively in a simulation study. The method is then applied to fitting models to a stratified multi-stage sample survey conducted by Iowa’s State Board of Education. In this study a small sample of school districts was selected from a two-way stratification of school districts. The survey strata serve as small areas for which hierarchical Bayesian estimators are suggested. Here the method is used to select a generalized linear mixed model for the survey data. Potential applications extend beyond the survey and education contexts.
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