A Bayesian Multilevel Regression Analysis of the PISA Data: Comparing Informative and Noninformative Priors

• In Event: Missing Data, Multicollinearity, and Variable Selection in Regression

Abstract

This paper compares informative and noninformative priors in the Bayesian multilevel modeling of the PISA data. To that end, a primary dataset from 2012 and a secondary dataset from 2003 are jointly analyzed to understand U.S. students' mathematics achievements using theoretically relevant predictors. The primary dataset serves to estimate a hierarchy of multilevel regression models with their (informative) priors derived from estimating related models using the secondary dataset under the traditional maximum likelihood method. For the purpose of comparison, the same Bayesian regression models are reanalyzed using only the primary data under noninformative priors. Finally, informative priors are found to reduce the uncertainty of Bayesian parameter estimate as demonstrated by smaller posterior standard deviations and narrower Bayesian confidence intervals.

Authors

• Hongwei Yang, University of West Florida

• Xing Liu, Eastern Connecticut State University

• Mark Malisa, University of West Florida

• Giang-Nguyen T. Nguyen, University of West Florida