Educational Applications of Hierarchical Linear Models: A Review

Abstract

The search for appropriate statistical methods for hierarchical, multilevel data has been a prominent theme in educational statistics over the past 15 years. As a result of this search, an important class of models, termed hierarchical linear models by this review, has emerged. In the paradigmatic application of such models, observations within each group (e.g., classroom or school) vary as a function of group-level or “microparameters.” However, these microparameters vary randomly across the population of groups as a function of “macroparameters.” Research interest has focused on estimation of both micro- and macroparameters. This paper reviews estimation theory and application of such models. Also, the logic of these methods is extended beyond the paradigmatic case to include research domains as diverse as panel studies, meta-analysis, and classical test theory. Microparameters to be estimated may be as diverse as means, proportions, variances, linear regression coefficients, and logit linear regression coefficients. Estimation theory is reviewed from Bayes and empirical Bayes viewpoints and the examples considered involve data sets with two levels of hierarchy.