ABSTRACT

In this chapter we present a brief introduction to the theory behind multilevel modelling. We illustrate the main points in our discussion with examples from our own and other research experience. These include examples of multilevel models with random slopes, growth curve models, multivariate models and crossclassified models. We do, however, limit our discussion to multilevel analysis with continuously distributed outcome variables. Readers interested in multilevel analysis with discrete (dichotomous and ordinal) rather than continuous outcome variables are referred to more extensive and advanced publications on multilevel analysis (Bryk and Raudenbush 1992; Goldstein 1995; Hox 2002; Snijders and Bosker 1999). Moreover, some effectiveness studies have made use of this type of multilevel model, so such further reading might be of particular use to readers of this volume (Kyriakides et al. 2009; Pustjens et al. 2004)

Research in the field of educational effectiveness often involves the analysis of data sets that are hierarchically structured. In these cases, two or more levels can be distinguished, with the units at the lower levels nested within the higher level units. The most well-known example of this is a data set of students nested within classrooms within schools. The hierarchical structure may be extended even further, for example, if one takes into account the nesting of schools within geographical units (such as local communities, regions or nations).