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Aranda-Ordaz quantile regression for student performance assessment

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  • Hakim-Moulay Dehbi
  • Mario Cortina-Borja
  • Marco Geraci

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.

Suggested Citation

  • Hakim-Moulay Dehbi & Mario Cortina-Borja & Marco Geraci, 2016. "Aranda-Ordaz quantile regression for student performance assessment," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(1), pages 58-71, January.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:1:p:58-71
    DOI: 10.1080/02664763.2015.1025724
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    References listed on IDEAS

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    1. Cassen, Robert & Kingdon, Geeta, 2007. "Tackling low educational achievement," LSE Research Online Documents on Economics 43735, London School of Economics and Political Science, LSE Library.
    2. Machado, Jose A F & Santos Silva, Joao M C, 2008. "Quantiles for Fractions and Other Mixed Data," Economics Discussion Papers 3550, University of Essex, Department of Economics.
    3. Geraci, Marco, 2014. "Linear Quantile Mixed Models: The lqmm Package for Laplace Quantile Regression," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 57(i13).
    4. Meghir, Costas & Rivkin, Steven, 2011. "Econometric Methods for Research in Education," Handbook of the Economics of Education, in: Erik Hanushek & Stephen Machin & Ludger Woessmann (ed.), Handbook of the Economics of Education, edition 1, volume 3, chapter 1, pages 1-87, Elsevier.
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    Cited by:

    1. Marco Centoni & Vieri Del Panta & Antonello Maruotti & Valentina Raponi, 2019. "Concomitant-Variable Latent-Class Beta Inflated Models to Assess Students’ Performance: An Italian Case Study," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(1), pages 7-18, November.
    2. Guilherme Pumi & Cristine Rauber & Fábio M. Bayer, 2020. "Kumaraswamy regression model with Aranda-Ordaz link function," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1051-1071, December.
    3. Diego Ramos Canterle & Fábio Mariano Bayer, 2019. "Variable dispersion beta regressions with parametric link functions," Statistical Papers, Springer, vol. 60(5), pages 1541-1567, October.
    4. Cristine Rauber & Francisco Cribari-Neto & Fábio M. Bayer, 2020. "Improved testing inferences for beta regressions with parametric mean link function," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 687-717, December.
    5. Marco Geraci & Alexander McLain, 2018. "Multiple Imputation for Bounded Variables," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 919-940, December.

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