Aranda-Ordaz quantile regression for student performance assessment

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. In this article a class of quantile regression models for bounded response variables is developed. The one-parameter Aranda-Ordaz 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 seven-year old children part of the Millennium Cohort Study.

Keywords:

• bounded variable
• transformation
• education
• Millennium Cohort Study
• marginal effect

AMS Subject Classification:

• 91G70

JEL Classification:

• C10

Acknowledgments

We are grateful to two anonymous reviewers for their helpful comments.

We thank José A.F. Machado and João M.C. Santos Silva for allowing us to cite their working paper about quantiles for fractions and other mixed data.

Mario Cortina-Borja would like to acknowledge the invaluable contribution that his mentor and greatly missed friend Francisco Aranda-Ordaz had in his education.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work was in part undertaken at Great Ormond Street Hospital/UCL Institute of Child Health which received a proportion of funding from the NIHR Biomedical Research Centres funding scheme of the UK Department of Health.

ORCID

Marco Geraci http://orcid.org/0000-0002-6311-8685