Multilevel Modelling for Cross-Classification and Multiple Membership Data

By Prof. Samuel Manda - Visiting Prof from Biostatistics Research Unit, South African Medical Research Council

Multilevel models are generalizations of linear and non-linear models where regression parameters are given a model, whose unknown parameters are also estimated from data. These models are particularly appropriate for research designs where data for subjects are organized at more than one level. Multilevel models can be used on data with many levels, although 2-level models are the most common. The dependent variable must be examined at the lowest level of analysis, usually at the subjects that are nested within contextual and aggregate higher level units.

Applications of multilevel models cover many kinds of data that have a hierarchical or clustered structure. As an example, children from same parents tend to be more alike in their physical and mental characteristics than children chosen at random from the children population. The children can be further nested within geographical areas or schools. Repeated measurements in longitudinal studies where an individual’s responses over time are correlated with each other can also be analyzed within multilevel modelling contexts. Multilevel models recognize the existence of such data hierarchies by allowing for residual components at each level in the hierarchy where the residual variance is partitioned into a between-level and a within-school component. The specific-level residuals represent unobserved level characteristics that affect subject outcomes at that level. The unobserved variables lead to correlation between outcomes for subjects from the hierarchical level.

Using a variety of applications, we illustrate the methodological elements of multilevel modelling. In particular, we highlight methodological extensions of multilevel modelling to fitted non-hierarchical data structures including cross-classification and multiple memberships.