Multilevel modelling glossary

• Cluster: A grouping containing lower level elements. For example in a sample survey the set of households in a neighbourhood.
• Cross classification: A structure where lower level units are grouped within the cells of a multiway classification of higher level units
• Design matrix: In the fixed part of the model, the matrix of values of the explanatory variables X. In the random part the matrix of explanatory variables Z.
• Explanatory variable: Also known as an ‘independent’ variable. In the fixedpart of the model usually denoted by X and in the random part by Z.
• Fixed part:That part of a model represented by Xß, that is the average relationship.
• Level:A component of a data hierarchy. Level 1 is the lowest level, for example students within schools or repeated measurement occasions within individual subjects.
• Level n variation: The variation among level n unit measurements.
• Multiple membership: A structure where a level unit may be nested within one or more higher level units.
• Nesting:The clustering of units into a hierarchy
• Random part:That part of a model represented by Zu, that is the contribution of the random variables, at each level.
• Response variable:Also known as a ‘dependent’ variable. Denoted by y.
• Unit:An entity defined at a level of a data hierarchy. For example an individual student will be a level 1 unit within a level 2 unit such as a school.

The above terms are courtesy of: Goldstein, H. (2003). Multilevel Statistical Models (3rd Edition). London, Edward Arnold: New York, Halstead Press.

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