Aranda-Ordaz quantile regression for student performance assessment

In education research, normal regression models may not be appropriate due to the presence of boundedvariables, 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 addressmodelling issues that arise when estimating conditional quantiles of a bounded response variable whoserelationship with the covariates is possibly nonlinear. This approach exploits the equivariance property ofquantiles and aims at achieving linearity of the predictor. This offers a flexible model-based alternativeto nonparametric estimation of the quantile function. Since the transformation is quantile-specific, themodelling 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 theMillennium Cohort Study.