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The use of sampling weights in M‐quantile random‐effects regression: an application to Programme for International Student Assessment mathematics scores

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  • Francesco Schirripa Spagnolo
  • Nicola Salvati
  • Antonella D’Agostino
  • Ides Nicaise

Abstract

M‐quantile random‐effects regression represents an interesting approach for modelling multilevel data when the researcher is focused on conditional quantiles. When data are obtained from complex survey designs, sampling weights must be incorporated in the analysis. A robust pseudolikelihood approach for accommodating sampling weights in M‐quantile random‐effects regression is presented. In particular, the method is based on a robustification of the estimating equations. The methodology proposed is applied to the Italian sample of the Programme for International Student Assessment 2015 survey to study the gender gap in mathematics at various quantiles of the conditional distribution. The findings offer a possible explanation of the low proportion of women in science, technology, engineering and mathematics sectors.

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  • Francesco Schirripa Spagnolo & Nicola Salvati & Antonella D’Agostino & Ides Nicaise, 2020. "The use of sampling weights in M‐quantile random‐effects regression: an application to Programme for International Student Assessment mathematics scores," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 991-1012, August.
    • Handle: RePEc:bla:jorssc:v:69:y:2020:i:4:p:991-1012
    DOI: 10.1111/rssc.12418
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    1. Nicole Schneeweis & Rudolf Winter-Ebmer, 2008. "Peer effects in Austrian schools," Studies in Empirical Economics, in: Christian Dustmann & Bernd Fitzenberger & Stephen Machin (ed.), The Economics of Education and Training, pages 133-155, Springer.
    2. Annamaria Bianchi & Enrico Fabrizi & Nicola Salvati & Nikos Tzavidis, 2018. "Estimation and Testing in M‐quantile Regression with Applications to Small Area Estimation," International Statistical Review, International Statistical Institute, vol. 86(3), pages 541-570, December.
    3. Sophia Rabe‐Hesketh & Anders Skrondal, 2006. "Multilevel modelling of complex survey data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(4), pages 805-827, October.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Davide Azzolini & Philipp Schnell & John R. B. Palmer, 2012. "Educational Achievement Gaps between Immigrant and Native Students in Two “New†Immigration Countries," The ANNALS of the American Academy of Political and Social Science, , vol. 643(1), pages 46-77, September.
    6. Jianqiang C. Wang & J. D. Opsomer, 2011. "On asymptotic normality and variance estimation for nondifferentiable survey estimators," Biometrika, Biometrika Trust, vol. 98(1), pages 91-106.
    7. Sevda Gürsakal & Dilek Murat & Necmi Gürsakal, 2016. "Assessment of PISA 2012 Results With Quantile Regression Analysis Within The Context of Inequality In Educational Opportunity," Alphanumeric Journal, Bahadir Fatih Yildirim, vol. 4(2), pages 41-54, September.
    8. Roland G. Fryer & Steven D. Levitt, 2010. "An Empirical Analysis of the Gender Gap in Mathematics," American Economic Journal: Applied Economics, American Economic Association, vol. 2(2), pages 210-240, April.
    9. Nikos Tzavidis & Nicola Salvati & Timo Schmid & Eirini Flouri & Emily Midouhas, 2016. "Longitudinal analysis of the strengths and difficulties questionnaire scores of the Millennium Cohort Study children in England using M-quantile random-effects regression," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(2), pages 427-452, February.
    10. Miyako Ikeda & Emma García, 2014. "Grade repetition: A comparative study of academic and non-academic consequences," OECD Journal: Economic Studies, OECD Publishing, vol. 2013(1), pages 269-315.
    11. C. Masci & F. Ieva & T. Agasisti & A. M. Paganoni, 2017. "Bivariate multilevel models for the analysis of mathematics and reading pupils' achievements," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(7), pages 1296-1317, May.
    12. World Bank, 2011. "World Development Report 2011 [Rapport sur le développement dans le monde 2011 : Conflits, sécurité et développement - Abrégé]," World Bank Publications - Books, The World Bank Group, number 4389, December.
    13. Angela Cipollone & Eleonora Patacchini & Giovanna Vallanti, 2014. "Female labour market participation in Europe: novel evidence on trends and shaping factors," IZA Journal of European Labor Studies, Springer;Forschungsinstitut zur Zukunft der Arbeit GmbH (IZA), vol. 3(1), pages 1-40, December.
    14. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    15. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    16. Bratti, Massimiliano & Checchi, Daniele & Filippin, Antonio, 2007. "Territorial Differences in Italian Students’ Mathematical Competencies: Evidence from PISA 2003," IZA Discussion Papers 2603, Institute of Labor Economics (IZA).
    17. Jones, M. C., 1994. "Expectiles and M-quantiles are quantiles," Statistics & Probability Letters, Elsevier, vol. 20(2), pages 149-153, May.
    18. Mariagiulia Matteucci & Stefania Mignani, 2014. "Exploring Regional Differences in the Reading Competencies of Italian Students," Evaluation Review, , vol. 38(3), pages 251-290, June.
    19. Kokic, Philip, et al, 1997. "A Measure of Production Performance," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(4), pages 445-451, October.
    20. Tommaso Agasisti & Francesca Ieva & Anna Maria Paganoni, 2017. "Heterogeneity, school-effects and the North/South achievement gap in Italian secondary education: evidence from a three-level mixed model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(1), pages 157-180, March.
    21. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    22. Ray Chambers & Hukum Chandra & Nicola Salvati & Nikos Tzavidis, 2014. "Outlier robust small area estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 47-69, January.
    23. World Bank, 2012. "World Development Report 2012 [Rapport sur le développement dans le monde 2012]," World Bank Publications - Books, The World Bank Group, number 4391, December.
    24. Beatrice Rangvid, 2007. "School composition effects in Denmark: quantile regression evidence from PISA 2000," Empirical Economics, Springer, vol. 33(2), pages 359-388, September.
    25. Susana Faria & Maria Conceição Portela, 2016. "Student Performance in Mathematics using PISA-2009 data for Portugal," Working Papers de Gestão (Management Working Papers) 01, Católica Porto Business School, Universidade Católica Portuguesa.
    26. D. Pfeffermann & C. J. Skinner & D. J. Holmes & H. Goldstein & J. Rasbash, 1998. "Weighting for unequal selection probabilities in multilevel models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 23-40.
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