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Multivariate multilevel analyses of examination results

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  • Min Yang
  • Harvey Goldstein
  • William Browne
  • Geoffrey Woodhouse

Abstract

Summary. In the study of examination results much interest centres on comparisons of curriculum subjects entered and the correlation between these at individual and institution level based on data where not every individual takes all subjects. Such `missing' data are not missing at random because individuals deliberately select subjects that they wish to study according to criteria that will be associated with their performance. In this paper we propose multivariate multilevel models for the analysis of such data, adjusting for such subject selection effects as well as for prior achievement. This then enables more appropriate institutional comparisons and correlation estimates. We analyse A‐ and AS‐level results in different mathematics papers of 52 587 students from 2592 institutions in England in 1997. Although this paper is concerned largely with methodology, substantive findings emerge on the effects of gender, age, intakes of General Certificate of Education pupils, examination board and establishment type for A‐ and AS‐level mathematics.

Suggested Citation

  • Min Yang & Harvey Goldstein & William Browne & Geoffrey Woodhouse, 2002. "Multivariate multilevel analyses of examination results," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 165(1), pages 137-153, February.
    • Handle: RePEc:bla:jorssa:v:165:y:2002:i:1:p:137-153
    DOI: 10.1111/1467-985X.00633
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    Cited by:

    1. Li Mingliang & Tobias Justin, 2005. "Bayesian Modeling of School Effects Using Hierarchical Models with Smoothing Priors," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(3), pages 1-33, September.
    2. Chipperfield, James O. & Steel, David G., 2012. "Multivariate random effect models with complete and incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 146-155.
    3. Stephane, ROBIN & Maresa, SPRIETSMA, 2003. "Characteristics of teaching institutions and students’ performance : new empirical evidence from OECD data," LIDAM Discussion Papers IRES 2003028, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    4. Pedro Luis do N. Silva & Fernando Antônio da S. Moura, 2022. "Fitting multivariate multilevel models under informative sampling," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1663-1678, October.
    5. Alinne Veiga & Peter W. F. Smith & James J. Brown, 2014. "The use of sample weights in multivariate multilevel models with an application to income data collected by using a rotating panel survey," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(1), pages 65-84, January.
    6. William J. Browne, 2022. "A celebration of Harvey Goldstein’s lifetime contributions: Memories of working with Harvey Goldstein on multilevel modelling methods and applications," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 753-758, July.
    7. Chiara Masci & Francesca Ieva & Tommaso Agasisti & Anna Maria Paganoni, 2021. "Evaluating class and school effects on the joint student achievements in different subjects: a bivariate semiparametric model with random coefficients," Computational Statistics, Springer, vol. 36(4), pages 2337-2377, December.
    8. Maresa, SPRIETSMA, 2006. "Regional school comparison and school choice : how do they relate to student performance ? Evidence from PISA 2003," Discussion Papers (ECON - Département des Sciences Economiques) 2006002, Université catholique de Louvain, Département des Sciences Economiques.
    9. Hauck, Katharina & Street, Andrew, 2006. "Performance assessment in the context of multiple objectives: A multivariate multilevel analysis," Journal of Health Economics, Elsevier, vol. 25(6), pages 1029-1048, November.
    10. Ferraro, Aniello & Cerciello, Massimiliano & Agovino, Massimiliano & Garofalo, Antonio, 2021. "Do public policies reduce social exclusion? The role of national and supranational economic tools," Structural Change and Economic Dynamics, Elsevier, vol. 57(C), pages 165-181.

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