Quantile Regression for Assessing Educational Interventions: Developing Critical Thinking Skills Among Elementary School Students

• Activity Number: 362
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Social Statistics Section
• Author(s): Mack Shelley* and Luke Fostvedt
• Companies: Iowa State University and Pfizer Inc. Global Research and Development
• Keywords: quantile regression ; science education ; critical thinking ; hierarchical linear models ; asymmetric Laplace distribution ; Bayesian estimation

Abstract

Data collection schemes with multiple source of variation are extremely common. However, extensions of quantile regression methods to these situations have not been thoroughly developed. There is a dearth of approaches that allow inferences to be made at multiple levels. This paper addresses a Bayesian approach at incorporating multiple levels into a quantile regression linear model using the Asymmetric Laplace Distribution (ALD). Traditional regression approaches provide inferences regarding the conditional mean, whereas quantile regression provides a framework through which the entire collection of conditional distributions can be characterized. This enables further inferences about the relationship between covariates and a response. Since the ALD includes the common loss function used for quantile regression in its kernel, it can be used for Bayesian estimation approaches that include both fixed and random effects in the model. This procedure is applied to model students' improvement in critical thinking associated with a new way to teach science in elementary school.