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Generalized linear mixed models for ordered responses in complex multilevel structures: effects beneath the school or college in education

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  • Antony Fielding
  • Min Yang

Abstract

Summary. The complexities of educational processes and structure and the need for disentangling effects beneath the level of the school or college are discussed. Ordinal response multilevel crossed random‐effects models for educational grades are introduced. Weighted random effects for teacher contributions are then added. Estimation methodology is reviewed. Specially written macros for quasi‐likelihood with second‐order terms are described. The application discusses General Certificate of Education at advanced level grades cross‐classified by student and teaching group within a number of institutions. The methods handle teacher effects where several teachers contribute to provision and where each teacher deals with several groups. Some methodological lessons are drawn for sparse data and the use of extra‐multinomial variation. Developments of the analysis yield conclusions about the sources of variation in educational progress, and particularly the effect of teachers.

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  • Antony Fielding & Min Yang, 2005. "Generalized linear mixed models for ordered responses in complex multilevel structures: effects beneath the school or college in education," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 159-183, January.
    • Handle: RePEc:bla:jorssa:v:168:y:2005:i:1:p:159-183
    DOI: 10.1111/j.1467-985X.2004.00342.x
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    References listed on IDEAS

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    1. M. Yang & H. Goldstein & A. Heath, 2000. "Multilevel models for repeated binary outcomes: attitudes and voting over the electoral cycle," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 163(1), pages 49-62.
    2. Germán Rodríguez & Noreen Goldman, 2001. "Improved estimation procedures for multilevel models with binary response: a case‐study," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(2), pages 339-355.
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    Cited by:

    1. George Leckie, 2009. "The complexity of school and neighbourhood effects and movements of pupils on school differences in models of educational achievement," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(3), pages 537-554, June.
    2. 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.
    3. J. R. Lockwood & D. McCaffrey, 2020. "Using hidden information and performance level boundaries to study student–teacher assignments: implications for estimating teacher causal effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1333-1362, October.
    4. Chan, Moon-tong & Yu, Dalei & Yau, Kelvin K.W., 2015. "Multilevel cumulative logistic regression model with random effects: Application to British social attitudes panel survey data," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 173-186.
    5. Philipp Ecken & Richard Pibernik, 2016. "Hit or Miss: What Leads Experts to Take Advice for Long-Term Judgments?," Management Science, INFORMS, vol. 62(7), pages 2002-2021, July.

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