Analysis of the Effects of School Variables Using Multilevel Models

Multilevel models allow data to be analysed which are hierarchical in nature; in particular, data which have been collected on pupils grouped into schools. Some of the associated variables may be measured at the pupil level, and others at the school level. The use of multilevel models produces estimates of variances between schools and pupils, as well as the effects of background variables in reducing or explaining these variances. One data set which has been analysed relates to the national surveys of mathematics carried out in England, Wales and Northern Ireland. In this case the basic unit of analysis was a pupil's performance in a group of items within one of 12 sub-categories of maths. Each pupil tackled two such item groups (or sub-tests) and thus a three-level model was required, with the levels representing sub-tests, pupils and schools. A number of background variables at both pupil and school levels were also measured, and interesting results were obtained when a multilevel model was fitted. The program used was a version of one developed by Professor H. Goldstein. A quite different data set related to pupils' responses to a questionnaire survey about their reactions to their current course of study. The dependent variable was a measure of pupils' satisfaction with the course derived from their responses, and other pupil level variables were also derived, relating to their school experiences and personal attributes. School level variables such as size and type of school were obtained from a schools data base. The program Hierarchical Linear Model (HLM) was used to model these data, using only two levels. The two multilevel program used have different strengths and capabilities, but are related in terms of the kinds of models that can be fitted. Such models can lead to greater insights into the relationships between school and pupil level variables, and their influence on pupil results or attitudes.