| Lu Lu
Iowa State University
Statistical methods for utilizing auxiliary data in educational surveys
FINAL REPORT
In many educational surveys that involve stratification and clustering structures, given the budget, time and resource restrictions, the surveys are usually designed to produce specific accuracy of direct estimation at high levels of aggregation. Sample sizes for small geographical areas or subpopulations are typically small such that direct estimates in these areas are very unreliable.
In the context of small area estimation, hierarchical Bayesian (HB) analysis is proposed to produce more reliable estimates of small area quantities than direct estimation. A method that benchmarks the HB estimates to the higher level direct estimates and measures the relative inflation of posterior mean squared error in the posterior predictions is developed to evaluate the performance of hierarchical models. Both numerical and graphical summaries of the posterior predictive discrepancy measures are available. The benchmarked HB posterior predictive model comparison method is shown to be able to select proper models effectively in an illustrative example. The method is then applied to fitting models to the IowaÕs State Board of Education transcript survey data. 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. The proposed method is used to select a generalized linear mixed model for analyzing the data. The Common Core variables were used as covariates in the models.
The methods proposed can be used to select models using predictor variables such as enrollment size and the common core variables in education studies. Additionally, ratio estimation methods and hierarchical modeling methods can use the common core variables as well. The hierarchical models and Bayesian analysis can improve on the direct estimation of small area statistics. The developed methodology can help practitioners make appropriate use of statistical models and covariate information to produce more reliable estimates of small area quantities for application in many educational surveys and studies.
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