ABSTRACT
Hierarchical regression models are useful as soon as there are predictors at different levels of variation. For example, in studying scholastic achievement we may have information about individual students (for example, family background), class-level information (characteristics of the teacher), and also information about the school (educational policy, type of neighborhood). Another situation in which hierarchical modeling arises naturally is in the analysis of data obtained by stratified or cluster sampling. A natural family of models is regression of y on indicator variables for strata or clusters, in addition to any measured predictors x. With cluster sampling, hierarchical modeling is in fact necessary in order to generalize to the unsampled clusters.
