Hierarchical Linear Models

Abstract

In applications of generalized linear models to education, observations at one level are frequently nested within units at another level. For example, we have measurements on students, who are located within a class, which is within a school, and so on. Methods for analyzing such data go back several decades, but new methods have led to many extensions and interesting ways of interpreting such models. These include models for multiple measures on individuals (such as longitudinal studies), and individuals nested within studies (for meta-analysis). These models also directly solve the aggregation problem: statistics on higher level units (e.g., correlations of school or classroom means) often do not equal (and may even be opposite in sign to) those for lower level units (both overall and within each higher level unit).