Uncovering important patterns of subject level school qualifications: a latent variable analysis of multiple cohorts of school data for England and Wales

General Certificates of Secondary Education (GCSEs) are the main school qualifications in England and Wales. Analysing GCSE outcomes is challenging because pupils study many subjects, each subject is awarded an individual grade, and there is no common or compulsory set of subjects. In this study we investigate inequalities in pupils' highly individualised school GCSE profiles using latent variable models, with data from the Youth Cohort Study of England and Wales (YCS). Four latent educational groups were identified. The identification of two distinctive groups with moderate levels of GCSE outcomes but different GCSE profiles, especially in science subjects, is an important new finding. The latent variable approach remains suitable for the numeric GCSE grading scheme (i.e., grades 1-9) first implemented in 2017, because the numerical grades are also discrete ordered categories. The approach is more broadly applicable to other educational systems where there is no compulsory set of subjects.