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

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.