Aranda-Ordaz Quantile Regression for Student Performance Assessment

• Activity Number: 318
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Mario Cortina-Borja and Hakim-Moulay Dehbi and Marco Geraci*
• Companies: University College London and Imperial College London and University of South Carolina
• Keywords: bounded variable ; transformation ; education ; Millennium Cohort Study ; marginal effect

Abstract

In education research, normal regression models may not be appropriate due to the presence of bounded variables, which may exhibit a large variety of distributional shapes and present floor and ceiling effects. Bearing this in mind we develop a class of quantile regression models for bounded response variables. The one-parameter Aranda-Ordaz (AO) symmetric and asymmetric families of transformations are applied to address modelling issues that arise when estimating conditional quantiles of a bounded response variable whose relationship with the covariates is possibly nonlinear. This approach exploits the equivariance property of quantiles and aims at achieving linearity of the predictor. This offers a flexible model-based alternative to nonparametric estimation of the quantile function. Since the transformation is quantile-specific, the modelling takes into account the local features of the conditional distribution of the response variable.

Our study is motivated by the analysis of reading performance in 7-year old children part of the UK Millennium Cohort Study.