Aranda-Ordaz quantile regression for student performance assessment. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Dehbi, Hakim-Moulay; Cortina-Borja, Mario; Geraci, Marco
• Is Part Of: Journal of applied statistics. Volume 43:Issue 1(2016)
• Page Start: 58
• Page End: 71
• Publication Date: 2016-01-02
• Subjects: bounded variable -- transformation -- education -- Millennium Cohort Study -- marginal effect; 91G70; C10; Statistics -- Periodicals; 519.5
• DOI: 10.1080/02664763.2015.1025724
• Languages: English
• ISSNs: 0266-4763

Abstract

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.